Interleaved Pfc Matlab

Circuits And Systems, 2016, 7, 307-326

Published Online April 2016 in SciRes. http://www.scirp.org/journal/cs

Http://Dx.Doi.Org/10.4236/Cs.2016.74027

How to cite this paper: Inba Rexy, A. and Seyezhai, R. (2016) Investigation of Current Control Techniques of AC-DC Inter- leaved Boost PFC Converter. Circuits and Systems, 7, 307-326. http://dx.doi.org/10.4236/cs.2016.74027

A. Inba Rexy1*, R. Seyezhai2

Received 6 March 2016; accepted 24 April 2016; published 27 April 2016 Copyright © 2016 by authors and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY).

Abstract

This paper presents the comparison of various current control strategies employed for an inter- leaved power factor correction (PFC) boost converter for improving the power quality. The major control strategies discussed in this paper are: peak current control, average current control, hys- teresis control, borderline current control and non-linear control. These strategies are imple- mented in MATLAB/SIMULINK and the performance of the proposed converter is compared under open loop and closed loop operation. From the results, the input current waveform was close to input voltage waveform implying improved power factor and reduced total harmonic distortion for nonlinear current control technique. Experimental results validate the proposed method.

Keywords

AC-DC Power Conversion, Power Factor Correction, Nonlinear Current Control, Control

1. Introduction

The power-electronics products are employed for a variety of applications such as power supplies for microelec- tronics, household electric appliances, electronic ballasts, battery charging, motor drives, power conversion cir- cuits, etc., but this leads to rich current harmonics at the supply side. Therefore, Power Factor Correction (PFC) is necessary for AC-DC converters in order to fulfill the requirements of international standards. PFC will re- duce the harmonics in the supply current and boost the efficiency of the system. Even though numerous methods have been suggested to resolve the problem of low power factor, it is important to make the supply power factor to unity. In order to meet the standards of IEC 6l000-3-2 Electromagnetic compatibility (EMC): harmonic *Corresponding author.

308

current limits, achieve high power factor and reduced harmonics, power factor corrected converters are com- monly employed in various types of switching power supply -. The continuous conduction mode (CCM) boost converter possesses many advantages such as low input current waveform distortion, high output voltage, high input power factor, less EMI noise and simple circuit construction, etc.

Interleaved boost converter is one of the most popular choices for high power factor converter. This type of converter provides an output voltage greater than the input voltage and also it operates at maximum duty ratio. The boost converter is supplied from a full wave rectified line voltage and operated so that the input current fol- lows the input voltage and it is generally preferred because of its simple construction. Power factor correction (PFC) - is necessary for AC-DC converters in order to accomplish the requirements of international stan- dards. PFC will decrease the harmonics in the supply current and raise the efficiency of the system. Even though a number of methods have been recommended to resolve the problem of power factor, it is essential to make the supply power factor closer to unity. Hence power factor corrected boost converter is very attractive, which eli- minates the filter from input side thereby achieving ripple free power in the AC line. Boost converter generally has at least two semiconductors and one energy storage element, a capacitor, inductor, or the two in combination.

Filters made of capacitors or in combination with inductors are normally added to the output of the converter which makes the circuit bulky. Hence to overcome this interleaved boost converters were suggested. Due to the absence of filter at supply side the converter is not bulky and hence it increases the power density of the conver- ter. The above said is achieved by employing a coupled inductor . As power densities continue to rise, interleaved boost designs become a powerful tool to keep input currents manageable and increase efficiency, while still maintaining good power density. With mandates on energy savings more common, interleaved con- struction may be the only way to achieve design objectives. The benefits of this approach are demonstrated by a two-phase boost converter design. A modified interleaved boost converter with a coupled inductor is also called as ripple steering technique which is also identified as coupled magnetic filters technique .

Various techniques are available for shaping the line current, and also they are supported by integrated cir- cuits -. These closed loop current control techniques provides very low current harmonic distortion, good performance, simple circuit construction and high efficiency. Therefore the shape of the current waveform is determined and found to be in line with the supply voltage waveform. The current control techniques offer improved performance and low input THD over existing open loop PFC schemes. Therefore various control techniques such as peak current control, average current control, hysteresis control, borderline control and non- linear current control for interleaved boost converter have been studied and analyzed. These techniques are si- mulated in MATLAB/SIMULINK and the feasibility of the proposed topology is experimentally verified. The objective of this paper is to improve the power factor of the proposed interleaved boost PFC converter.

The paper is organized as follows: Section 2.1 gives a brief idea of the interleaved boost converter. Section 2.2 analyzes the effect of the ripple steering technique in detail. Section 3 deals about the design of interleaved boost converter. Section 4 analyzes the operation of interleaved boost PFC converter with different current con- trol strategies. Section 5 gives the comparison between the proposed control techniques and the open loop con- figuration of interleaved boost PFC with ripple steering technique. The analysis is made in terms of input current, input voltage, output voltage and total harmonic distortion with the help of simulation results. A prototype has been built and tested, and the experimental results are presented in Section 6.

2.1. Interleaved Boost Converter

Power factor correction (PFC) interleaved boost converter is a popular topology for high level switching power supply to improve the power factor (PF). An interleaved boost converter provides benefits of component availa- bility, high efficiency, high power density and low harmonics compared to conventional converters. Hence it has been extensively used in numerous applications. The important features for these type of converters is the cur- rent cancellation effect thereby reduces the size, weight and cost of the filters. It also identifies the differential mode EMI noise hence suitable for input filter design, input and output side capacitor selection.

The interleaved boost converter is simply two traditional boost converters with half the power rating as a re- sult the input bridge rectifier must have the same power rating as the conventional power factor corrected boost converter. And also design equations will be alike to that of conventional converters. Interleaved boost conver- ters are usually employed for high input-current and high input to output voltage conversion applications. The

309

added benefit of interleaving is that ripple currents are reduced at both input and output side. There is an in- creased efficiency by splitting the output current into “n” pathways; considerably it reduces the power and in- ductor losses. Here the interleaved structure is presented for boost converter to improve the efficiency of the PFC converter -. This is mainly done for the applications of DC voltage smaller than the AC-side vol- tage.

2.2. Interleaved Boost Converter with Ripple Steering Technique Interleaved boost converter with ripple steering technique is employed to achieve active power-factor correction. This ripple steering technique is also called as coupled magnetic filter technique and it is implemented to IBC topology in this paper. The concept of zero-ripple or ripple-free input current is not new. It was originally used to reduce weight and increase power density of the converter. Generally, a zero-ripple phenomenon is achieved by using the coupled inductor technique in a modified boost converter. Based on the zero-ripple input current concept, various PFC converters with separate inductors and EMI filter requirements can be found in the litera- ture -. As earlier studied, a modified boost converter with a coupled inductor can provide a smaller converter size compared with conventional boost converter. The application of the zero-ripple current pheno- menon is of significant importance in switching converters, where there are few reasons why it is necessary to minimize inductor ripple currents. It reduces the stress on converter capacitors, resulting in either minimum power loss or more comfortable filtering requirements. And also most of the converter topologies have a pulsat- ing current at input or output, or at both. Advantages of interleaving, such as higher efficiency, reduced input and output ripple and also inductor count and the switches count are reduced. The conventional inductor is re- placed by a coupled inductor and a blocking capacitor here. Importance is given to the application of ripple steering to power factor corrected boost converter. Figure 1 shows the proposed PFC boost converter with a coupled inductor and a blocking capacitor. There is a fall in noise, size and complexity of filters by adapting the proposed technique. Although the control technique is similar to that of a conventional converter, there is some variation in power stage transfer function. This is done by replacing the inductor in a conventional boost con- verter by a coupled inductor and a blocking capacitor. Figure 1 shows the modified boost converter with ripple steering technique.

3. Design Equation For Ibc

Designing an interleaved boost converter includes the following steps:

3.1. Choice Of Duty Ratio

Since the number of phases chosen in this paper is two, 50% of the duty cycle will be the best choice. And also D = 0.5 gives less ripples when compared to other duty ratios. The duty ratio is calculated as,

In

V denotes the input voltage in volts and D denotes the duty ratio.

C

Figure 1. Interleaved boost converter with ripple steering technique.

3.2. Optimal Number Of Phases

This paper uses two phases, as the number of phases is increased the ripples will be minimum. But increasing the number of phases will increase the cost and complexity of the circuit. Therefore the number of phases is chosen as two.

3.3. Design Of Inductance And Capacitance

The inductor and capacitor values can be found using the formula given below.

O

V denotes the output voltage in volts, D denotes the duty ratio, R denotes resistance in Ω, T denotes

∆

denotes the change in the output voltage.

S

V denotes the source voltage in volts, D denotes the duty ratio, F denotes the frequency in hertz and

∆

denotes the inductor current ripple in ampere. 4. Current Control Strategies for Interleaved Boost Converter with Ripple Steering

Technique

The main objective of this paper is to present the current control design techniques and experimental results for the proposed converter. An open loop control technique is often used in simple processes because of its simplic- ity and low cost, especially in systems where feedback is not significant. Generally, to obtain a more accurate control of the circuits, closed loop systems are designed to automatically achieve and maintain the desired out- put condition by comparing it with the actual condition. It does this by generating an error signal which is the difference between the output and the reference input. By adopting current control techniques , the power factor obtained in the open loop configuration of the converter can be enhanced. The advantage of current con- trol techniques over voltage control techniques are, it provides an additional inner control loop control. The in- ductor current is sensed and used to control the duty cycle. An error signal is generated by comparing output voltage with reference voltage. Then this error signal is used to generate control signal. The inductor current is then sensed and compared with control signal to generate the duty cycle of the switch and drive the switch of the converter. If the feedback loop is closed, the inductor current becomes proportional with control signal and the output voltage becomes equal to reference voltage. Using the feedback and feed forward loops, lower harmonic profile can be maintained. The general control principle of the controller is that the supply current is forced to track a generated sinusoidal reference so that the converter draws a sinusoidal current; thereby improving the power factor. Many current control strategies have been reported in the literature. The classification of current control strategies namely discontinuous inductor current mode (DICM) where the inductor current reaches zero during a cycle and continuous inductor current mode (CICM) where the inductor current does not reach zero during a cycle and energy is stored in the inductor. To operate the converter as a power factor corrector, consider continuous conduction mode: as the current stress and current ripple are minimum in this mode -. A number of continuous inductor current mode control strategies such as peak current control, average current control, hysteresis current control, borderline current control and non-linear control are implemented and ana- lyzed for the proposed converter.

4.1. Peak Current Control

A schematic circuit diagram of PFC interleaved boost converter under peak current control is presented in Figure 2. The switch turns on with a constant frequency and it can turn off until inductor current reaches a level set by the outer loop. Therefore, instant over-current switch protection is easier, but there is very noise sensitive control. A compensating ramp is always required to add, when the duty cycle exceeds 0.5, otherwise the control is inherently unstable. The switch is getting turned on with a fixed frequency by a clock signal and is turned off

Ff

Figure 2. Control circuit for peak current control. when the sum of the positive ramp of the inductor current (i.e. the switch current) and an external ramp (i.e. compensating ramp) touches the sinusoidal current reference. Usually, this reference can be attained by multip- lying a scaled replica of the rectified line voltage vg times the output of the voltage error amplifier, which sets the current reference amplitude. In this way, the reference signal is naturally synchronized and always propor- tional to the line voltage, which is the condition to obtain unity power factor. Whenever the inductor current crosses zero, switch is turned ON and as it reaches the reference current, the flip-flop is reset and the switch is turned OFF. Obviously the ramp compensation can improve the quality of the input line current, which means the amplitude of the ripple is decreased significantly. Owing to the large output capacitance, the output voltage ripple can be neglected. Therefore, the time-varying mathematical mode of PFC boost converter can be ex- pressed as a first order differential equation as follows:

In

V denotes the root mean square value of the line voltage.

O

V is the DC output voltage, T is the switching cycle and D is the duty cycle.

4.2. Average Current Control

In most of the power electronic converter applications the output variable is the voltage and is involved in the outer loop. The variable within the inner loop is current, this is the reason this technique is called as average current control technique. The average current controlled interleaved boost PFC converter, is designed to oper- ate in CCM, it may transit to DCM when the load becomes light. Figure 3 shows the main circuit and control block diagram of the average current controlled converter. It uses voltage control loop and current control loop.

C

Figure 3. Control circuit for average current control. Firstly the inductor current is sensed and filtered by a current error amplifier whose output drives a PWM mod- ulator. Hence the inner current loop tends to limit the error among the average input current ig and the reference.

The converter works in CICM, so the same considerations done with regard to the peak current control can be applied. The average of inductor current is taken as reference and the inductor current is forced to go after it. The switch is turned ON whenever the inductor current reaches zero and switch is turned OFF when the inductor current falls below the reference.

We know that the rectified input voltage of the boost converter can be expressed as follows:

In

ω are the root mean square value and angular frequency of the input voltage respectively. The average value of the inductor current is programmed to sinusoidal shape for achieving the PFC function.

Under different input voltage and load conditions, the average current controlled technique may operate in all CCM or partly CCM/DCM. When the converter operates in CCM, the duty cycle

Where

sf is the switching frequency.

4.3. Hysteresis Control

Figure 4 shows an alternative control technique called hysteresis control, which is proposed and analyzed . Among the various control methods, hysteresis current control is the extensively used technique owing to its noncomplex implementation, enhanced system stability, fast response, less distortion in input current waveform and regulating the output voltage. This technique is believed to exhibit greater stability. According to this con- trol technique, when the inductance current is less than the lower current reference, power switch is turned ON

C

Figure 4. Control circuit for hysteresis control. and when the inductance current is more than the upper current reference, power switch is turned OFF. The boost converter is being operated at continuous current mode (CCM). For the hysteresis control, the inductance current is switching at a variable switching frequency. The switch must be turned ON while zero crossing of the line voltage for restraining very high switching frequency. In order to avoid too high switching frequency, the switch can be kept open near the zero crossing of the line voltage so introducing dead times in the line current.

4.4. Borderline Control

In this type of control approach the ON time of the switch will remain constant during the line cycle and the switch is turned ON when the inductor current falls to zero. Therefore the converter operates at the boundary between Continuous and Discontinuous Inductor Current Mode. The freewheeling diode is turned OFF softly and the switch is turned ON at zero current. So the commutation losses are also reduced. And also the higher current peak increase the device stresses and conduction losses will lead to heavier input filters. This is a type of hysteretic control in which the lower reference IV, ref is zero anywhere. The principle scheme is shown in Fig- ure 5. The instant input current is constituted by a sequence of triangles whose peaks are proportional to the line voltage. Thus, the average input current becomes proportional to the line voltage, this characterizes this control as an automatic current shaper technique. Some of the merits of this technique are: compensation ramp is not necessary, no need of a current error amplifier and switch current limitation can be introduced.

4.5. Nonlinear Carrier Control

Nonlinear carrier controllers are proposed for high power factor boost rectifiers with low total harmonic distor- tion . In this type of controllers, the duty ratio is determined by comparing a signal derived from the main switch current with a periodic nonlinear carrier waveform. As a result, the average input current follows the in- put line voltage. This technique is suitable for boost converters operating in the continuous conduction mode.

The proposed controller obtains the duty ratio in each switching period from the comparison of the negative ramp carrier waveform and the sensed inductor current signal as shown in Figure 6 and sensed switch current signal as shown in Figure 7. So, the input voltage sensor, the error amplifier in the current feedback loop, and the multiplier as used in the conventional control technique are not required.

Comparator

Figure 5. Control circuit for borderline control.

Ff

Figure 6. Control circuit for non-linear current technique-inductor current sensing.

5. Simulation Results

The simulation results of the different current control strategies for interleaved boost converter are discussed here. The converter is designed with the simulation parameters as shown in Table 1; The performance of the in- terleaved boost converter is examined by computing parameters such as Total Harmonic Distortion (THD), Distortion factor Kd, Displacement factor Kθ and the power factor. Two phase interleaved boost converter with ripple steering technique for different control techniques are simulated using MATLAB/SIMULINK.

Ff

Figure 7. Control circuit for non-linear current technique-switch current sensing. Table 1. Simulation parameters.

0.5

For an ideal sinusoidal input voltage, the power factor can be expressed as the product of distortion factor and the displacement factor.

=

, which is called as displacement factor. The distortion factor

D

K is the ratio of the fundamental root mean-square current

I

. The displacement factor Kθ is the cosine of the displacement angle φ between the fundamental input current and the input voltage. The following equations link total harmonic distortion to power factor:

(13)

where φ is the angle between voltage and current, PF is the power factor, THD is the total harmonic distortion. The simulation results of the interleaved boost converter with ripple steering technique are shown in Figure 8. From Figure 8(c), it is clear that the total harmonic distortion of the proposed open loop configuration is 12.17% which is very less compared to conventional methods.

Figure 9 shows the simulation results of peak current control technique. The total harmonic distortion is found to be 11.63%.

(C)

Figure 8. Simulation results of interleaved boost converter with ripple steering tech- nique (open loop) (a) Supply voltage and supply current (b) Output Voltage (c) FFT analysis of current.

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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