Zvs Converter Design Matlab

Abstract—This paper proposes a new integrated magnetics (IM) design for an isolated zero-voltage-switching (ZVS) Ćuk converter (IZCC). In this design, six magnets are wound onto a single magnetic core, and to minimize magnetic core size and losses, both direct current (DC) and alternating current (AC) flux cancellations are considered. The DC flux is fully cancelled, and the AC flux must be cancelled until a limited value such that the input and output inductor currents have enough ripple to provide the conditions for achieving ZVS on all switches. Therefore, the value of the coupling coefficients (CC) between the windings should be considered such that the minimum ripple to achieve ZVS for all the switches is available. The design is implemented on a simple magnetic U-core, and the CC values are specified based on the winding locations and arrangement. To validate the idea experimentally, a hardware prototype is proposed with a power of 0.5 kW, a switching frequency of 150 kHz, and a peak efficiency of 97.25%.

Inductors,

coupling coefficients, ZVS, flux cancellation.

I. Introduction

Passive components play a critical role in power conversion systems . These components primarily include magnets and capacitors. Magnetics are components that provide energy savings, isolation, voltage conversion, and filtering. Depending on the type of power electronics converter, the number of these magnetics could change. Therefore, the way of designing and implementing these components has a direct effect on the converter operation and performance .

Besides their importance in power conversion, magnetics also significantly affect converter volume and efficiency. The magnetics are usually bulky components that need to be designed properly . There are different approaches to efficiently and compactly designing magnetic components in power converters. The conventional approach is a discrete approach, in which each magnetic is designed with a separate magnetic core. Although this approach is simple, it requires more numbers of cores, and the cores need more volume, which affects the power density . Besides that, adding more magnetic cores increases the cost of components and also, and each core has its own core losses, which increases the overall losses .

To overcome the mentioned problems of the discrete approach in magnetic designs, the approach of integration of magnetics in a single core has been proposed . Although this approach increases the complexity in design, it helps in reducing the number of utilized cores and increasing the power density, and it can also be effective in reducing the losses as well . There are different approaches to integrating magnetics into a converter. The integration of the resonant inductor with the transformer in the resonant converters is one of the common approaches for increasing the power density and

Reducing Component Count And Cost . However, This

approach may come at the expense of increased core loss of the transformer and deteriorate the performance of the power

Conversion System . The References Shows

the integration of inductors in interleaved boost converters with directly coupled inductors (CI). However, the direct-coupled inductors approach reduces component count and cost, but the core tends to saturate, requiring a larger core, especially in high- power applications.

Flux cancellation in the IM design is the approach to reduce the losses and increase the power density . The flux cancellation includes two types: DC and AC flux cancellation.

The DC flux in the magnetic core is effective in increasing the core volume, and therefore, DC flux cancellation helps in

Reducing The Core Volume . However, In These

references, DC flux cancellation approaches have increased the AC current ripple, thereby increasing core losses. The AC flux is not only effective in the core volume, but it is also the cause of the core losses because the core losses are related to the flux density variations . , show the AC flux cancellation approach. In , it is shown that the current ripple in the input and output inductors can be eliminated by integrating the inductors with the transformer windings. Although this approach reduces core losses, the DC flux remains, preventing a reduction in core volume.

There are different types of IM designs to reach both AC and DC flux cancellation on a specific E core in that both inductors are wound on the center limb. However, the leakage inductor in this approach is very small, and an auxiliary inductor is needed to create more ripple. In order to adjust the current ripple and reach both AC and DC flux cancellation, the reference has proposed the IM design on a U core. In this approach, DC flux cancellation can be easily achieved with a negative CC, and the amount of AC flux cancellation can be adjusted based on the winding arrangement and location.

However, this approach is applicable when the inductor current waveforms are aligned and vary together. Reference narrated an IM approach for an isolated Ćuk converter. This approach uses the transformer windings solely for AC flux cancellation, with operation under hard-switching conditions. As shown, the CI itself can cancel current ripples at a certain value, and to achieve zero ripple in the inductor currents, the input and output inductor windings need to be integrated with the transformer windings. To make the Ćuk converter operate in a soft-switching condition, the reference

2

proposed an IM design approach with ZVS achievement, but this approach is not applicable to high-power applications due to increased circulating current, and also, the proposed IM structure helps only with AC flux cancellation. The other approach to making ZVS Ćuk is the proposed IZCC topology shown in Fig. 1 and reference . By adding auxiliary circuits and a resonant inductor to the isolated Ćuk converter, the modes of operation will change, with two additional modes emerging.

Therefore, the way magnetics are integrated for AC flux cancellation across all modes of operation needs to change. The approach proposed in for the isolated resonant Ćuk converter utilizes both winding and core sharing to achieve DC and AC flux cancellations. In this approach, the resonant inductor is not integrated with the other magnetics, and the AC flux cannot be cancelled in phase-shift modes. Therefore, the current ripples are not very controllable and cannot be completely cancelled.

Fig. 1. Izcc Topology With The Magnetics Box

To address the aforementioned problems, this paper proposes an IM design that integrates all six windings into a single core and uses resonant inductors (RIs) to cancel ripple across all operating modes. All the windings are wound on a single U- core. Adjusting the proper CCs between the windings is critical to have the desired amount of ripple cancellation and proper operation of the IZCC. As mentioned in and , the input and output inductor currents need to have a minimum ripple to achieve ZVS on all switches. This is crucial when the converter operates at a high switching frequency. Therefore, the winding arrangement on the core should be such that not only is DC flux cancellation achievable, but also the CCs are adjusted to minimize ripple in the input and output inductors' current, thereby enabling ZVS. Thus, all the magnetics are integrated into a single core, and DC and AC flux cancellation is also achievable. These conditions reduce core volume, losses, costs, and the number of components.

To our knowledge, there is no prior work on integrating the different types of magnetics into a single, simple U-core that achieves both DC and AC flux cancellation and ensures ZVS for all switches. As such, the main contributions of the study

Are As Follows:

1) Integrating all six magnetic windings of the IZCC on a single U core and winding arrangement such that both DC and AC flux cancellation happen in the magnetic core,

Besides Proper Operation Of The Converter;

2) Achieving ZVS on all the switches by adjusting the CCs such that the minimum current ripples are available for

Satisfying The Zvs Conditions; And

3) 43% reduction in core volume, besides improvement in efficiency in the designed IM compared to the IZCC operation with discrete magnetics design.

Ii. Im For Soft Switching

The AC flux cancellation in the IM design should be such that neither affects the overall operation of the converter nor increases converter losses, such as switching losses, especially when the converter operates at a high switching frequency.

Therefore, the proposed approach in needs to meet the soft- switching requirements. The IZCC topology is the ZVS version of the isolated Ćuk converter. This converter has four modes of operation, as shown in Fig. 2 the input and output inductor currents are not aligned at modes 1 and 3. Also, as shown in the transformer voltage waveforms in this figure, the transformer is zero in these two modes of operation. Additionally, when the DC flux of the CI is cancelled inside the core, the AC flux direction changes from positive to negative, and the transformer windings will not be able to cancel the inductors’ fluxes when their flux directions change because the transformer windings’ fluxes are always in one direction and only their values change.

Therefore, integrating transformers with input and output inductors for AC ripple cancellation is not applicable when DC flux cancellation is desired. Thus, another winding arrangement and integration approach is needed.

This paper proposes a new integration of magnetics in the IZCC to achieve not only DC flux cancellation but also AC flux cancellation across all modes of operation. In this approach, the input and output inductors are coupled to form CI, and the RIs are also integrated on the core to help cancel AC flux. The CI will perform DC flux cancellation and AC flux cancellation in two operational modes (2 and 4). The RIs are added to cancel the AC flux in the other two modes of operation that the CI cannot perform (modes 1 and 3). The transformer is also integrated with the other magnetics with a high coupling between the primary and secondary windings. It reduces the magnetizing flux to a level that does not affect the operation of the CI and RIs. The transformer is integrated on the same core to not only reduce the overall magnetics volume but also help stabilize converter operation.

This approach offers flexibility, allowing the coupling between any two windings to be adjusted to control ripple cancellation. As the IZCC will operate at a high switching frequency, it is essential to achieve soft switching across all switches to achieve high efficiency. As the ZVS conditions rely on the input and output inductor current ripples in IZCC, there should be a tradeoff between the amount of current ripple cancellation and the ability to achieve ZVS on all switches. The current ripple on the CI currents increases the core losses.

Therefore, a comparison of core and switching losses at different switching frequencies is needed to determine which is dominant and decide whether to prioritize core loss reduction or achieving ZVS on the switches.

As Shown In

Fig. 1, the IZCC converter is drawn with a magnetics box. This box has six magnetic windings, which are input (𝐿𝑖𝑛) and output (𝐿𝑜) inductors, primary (𝐿𝑟1) and secondary (𝐿𝑟2) side resonant inductors, primary (𝑇1) and secondary (𝑇2) windings of the transformer. These magnetics can be in different

3

integrated or discrete combinations. The magnetics box should be designed so that it does not affect the converter's operation. Fig. 2 shows the IZCC operation waveforms considering all discrete magnetics. The secondary side switches (𝑆𝑠1, 𝑆𝑠2) do the switching by a phase shift delay (𝜌𝑇𝑠𝑤) after the primary side switches (𝑆𝑝1, 𝑆𝑝2) turned off respectively. As can be seen in this figure, 𝜌 is the phase shift ratio and 𝑇𝑠𝑤 is the switching period. There are two duty cycle ratios for the primary (𝑑𝑝) and secondary (𝑑𝑠) side switches. The switching sequence for all types of discrete or integrated magnetics is the same as Fig. 2.

In , all modes of operation are proposed for discrete magnetics. In here, four of the main modes of operation are considered, as the deadtime modes can be ignored compared to the main modes.

Fig. 2. IZCC waveforms of operation considering discrete magnetics

In , A Complete Model Of The Izcc Converter Is

proposed, and based on the model, the ZVS conditions for the switches in IZCC are governed by (1)-(4). In these conditions, 𝐶𝑜𝑠𝑠 is the switch’s output capacitor, 𝑉𝐶𝑇𝑃 is the average value of the primary side of the auxiliary capacitor. 𝑉𝐶𝑇𝑆 is the average value of the secondary side of the auxiliary capacitor. 𝑡𝑑𝑏 is the deadtime between each complementary switch. 𝐼𝐿𝑖𝑛 is the average value of the input inductor current. 𝐼𝐿𝑜 is the average value of the output inductor current. ∆𝐼𝐿𝑖𝑛 is the ripple value of the input inductor current. ∆𝐼𝐿𝑜 is the ripple value of the output inductor current . Parameters 𝑖𝐿𝑟(𝑡0) to 𝑖𝐿𝑟(𝑡3) are the initial values of the resonant inductor current at each mode of operation. It is assumed that 𝐿𝑟2 is transferred to the primary side and is combined with 𝐿𝑟1 and them 𝐿𝑟= 𝐿𝑟1 + 𝑛2𝐿𝑟2, where, 𝑛 is the transformer turns ratio.

(4)

The initial values of 𝑖𝐿𝑟(𝑡0)-𝑖𝐿𝑟(𝑡3) are specified as (5) to

′ = 1 −𝑑𝑠, And 𝐼𝐿𝑖𝑛

and 𝐼𝐿𝑜 are the average values of the input and output inductor currents.

(8)

In (5) to (8), the expressions of the auxiliary capacitors

(10)

These equations are derived from the volt-second balance equations for the input and output inductor voltages. In these equations, 𝑉𝑖𝑛 is the DC input voltage and 𝑉𝑜 is the DC output voltage.

A. Ci Structure

As can be seen in Fig. 2, each of the input and output inductor currents (𝑖𝐿𝑖𝑛(𝑡) , 𝑖𝐿𝑜(𝑡)) has a DC value (𝐼𝐿𝑖𝑛, 𝐼𝐿𝑜) plus an AC ripple (2∆𝐼𝐿𝑖𝑛, 2∆𝐼𝐿𝑜) on it. These two types of currents create DC and AC fluxes inside their related magnetic core for each of the 𝐿𝑖𝑛 and 𝐿𝑜 which causes core losses and raises the core saturation limit. DC and AC flux cancellation approaches can help reduce the core saturation limit, allowing us to use a

4

smaller core and mitigate core losses. Therefore, integration of 𝐿𝑖𝑛 and 𝐿𝑜 could help in this regard. Fig. 3 shows the IZCC topology with coupling of 𝐿𝑖𝑛 and 𝐿𝑜 which are the CI. As shown in this figure, both inductors are wound on a U core, and the sign of the created fluxes from the 𝐿𝑖𝑛 and 𝐿𝑜 are in opposite directions and therefore can cancel each other. The created fluxes contain both DC and AC fluxes.

The DC fluxes can be easily cancelled, and the AC flux depends on the directions of the current ripple each time. If both currents are increasing or decreasing, the fluxes can cancel each other; otherwise, they add.

Fig. 3. The CI instructor for 𝐿𝑖𝑛 and 𝐿𝑜 in IZCC. 4. The IZCC waveforms considering the CI structure In IZCC, 𝜌 is an essential parameter for the power transfer and output voltage regulation . As shown in Fig. 2, the directions of 𝑖𝐿𝑖𝑛(𝑡) and 𝑖𝐿𝑜(𝑡) are not the same in modes 1 and 3, and therefore, their AC fluxes will be additive in these two modes of operation, as shown in the CI in Fig. By considering CI in the IZCC topology, the waveforms of the 𝑖𝐿𝑖𝑛(𝑡) and 𝑖𝐿𝑜(𝑡) in Fig. 2 changes to Fig. As can be seen in this figure, the slopes of 𝑖𝐿𝑖𝑛(𝑡) and 𝑖𝐿𝑜(𝑡) in modes 1 and 3 are more than the other two modes of operation. This is due to the effect of additive AC fluxes in modes 1 and 3. The additive AC fluxes directly affect current ripples within a short time, thereby increasing the current slope.

B. Cc And Current Ripple In Ci

Specifying CC is the key to determining the amount of ripple cancellation or addition in the input and output inductor currents. Fig. 5 shows the equivalent circuit of the CI. By applying Kirchhoff's Voltage Law (KVL) in each input and output side loops, their voltage equations are determined to be

(9)

By considering a conversion ratio of 1 (i.e., 𝑛= 1), in Fig. 5, the relation between the mutual inductance (𝐿𝑖𝑜) and the magnetizing inductance (𝐿𝑚) is as (10). The relations between the input, output open circuit inductances (𝐿𝑖𝑛, 𝐿𝑜), leakage inductances (𝐿𝑙𝑖𝑛, 𝐿𝑙𝑜) and 𝐿𝑚 are as (11). Equation (12) determines the CC between 𝐿𝑖𝑛 and 𝐿𝑜 which is 𝑘𝑖𝑜 .

(12)

In the symmetrical (balanced) ripple, 𝐿𝑖𝑛=𝐿𝑜=𝐿 and, therefore, from (10)-(12), the relations between CI leakage inductances (𝐿𝑙𝑖𝑛, 𝐿𝑙𝑜), 𝑘𝑖𝑜, 𝐿𝑚, and L are found to be

(14)

Therefore, from (9)-(14), the state space equations for the CI can be driven by (15).

(15)

From (15), the input and output inductor currents' slopes can

(16)

As can be seen in Fig. 4, 𝑖𝐿𝑖𝑛 and 𝑖𝐿𝑜 waveforms are linear

5

and, therefore, from (16), the input and output inductor current ripples (∆𝑖𝐿𝑖𝑛, ∆𝑖𝐿𝑜) in each mode of the operation can be found as (17). In these equations, ∆𝑡 is the time duration of each operating mode.

(17)

As shown in Fig. 5, the relation between 𝑖𝐿𝑖𝑛, 𝑖𝐿𝑜 and the magnetizing current (𝑖𝐿𝑚) is as (18). In this equation, the conversion ratio is one (𝑛= 1).

(18)

From (18) and (17) the magnetizing current ripple (∆𝑖𝐿𝑚) is obtained as (19).

(19)

As seen from (17) and (19), the ripples are related to the 𝑘𝑖𝑜, and by properly adjusting the 𝑘𝑖𝑜, the desired current ripples can be achieved. As can be seen in Fig. 4, the input and output inductors' currents have different ripples in each mode of operation. It can be confirmed from (17) as well. From (9), (10) and Fig. 4, the values of the 𝑉𝐿𝑖𝑛 and 𝑉𝐿𝑜 in each mode of the operation are as (20) and (21). And the value of ∆𝑡 in each mode from Fig. 4 is as (22).

{

𝜌𝑇𝑠𝑤 [𝑀𝑜𝑑𝑒𝑠 1]

(22)

Fig. 6 shows the effect of 𝑘𝑖𝑜 on the input, output, and magnetizing inductor current ripples in four modes of operation for the IZCC. As can be seen in this figure, by increasing the value of 𝑘𝑖𝑜, the ripple currents for modes 2 and 4 decrease in both input and output inductor currents, whereas they increase for modes 1 and 3 in both currents. Thus, using only the CI in IZCC cancels the AC flux in two modes of operation and adds it in the other two; therefore, core losses cannot be mitigated.

A. Integration Of Ci And Resonant Inductors

As mentioned in the section IV part A, the AC fluxes are additive in modes 1 and 3. Fig. 4 shows that the resonant inductor's voltage (𝑉𝐿𝑟1(𝑡), 𝑉𝐿𝑟2(𝑡)) have their peak values during these two modes, and also, the resonant inductor's current (𝑖𝐿𝑟1(𝑡), 𝑖𝐿𝑟2(𝑡)) varies from positive to negative or vice versa. Therefore, these two inductors can be used to cancel flux Fig. 6. Input and output inductor current ripple variations based on the coupling

Coefficient (K) Changes

and thus ripple during modes 1 and 3. Fig. 7 shows the IZCC topology with the CI and RIs integrated on a core. Thus, the ripple cancellation can be achieved in all modes of operation.

Fig. 7. IZCC topology with the integration of CI and Ris

B. Full Im Structure

Although the RIs help in ripple cancellation at modes 1 and 3, they are additive at modes 2 and 4, and their flux can affect the CI's operation at those modes. Therefore, additional windings should be used to mitigate the effect of RIs in modes 2 and 4. In the Full IM structure, the transformer is also integrated with CI and RIs in this regard. Fig. 8 shows the IZCC topology with the IM structure. In the IZCC topology, the transformer must be designed with a high-value CC between the primary and secondary windings, and the RIs are then designed separately to provide flexibility for winding relocation and arrangement.

Fig. 8. Izcc Topology With Im Structure

Based on the IZCC operation, the sign of the CCs between every two windings should be as Table I. The IM winding arrangements should be such that the sign of the CCs between every two windings is as shown in this table. These signs come from the values of the current and the voltages from Fig. 4 and the necessity of some signs to be positive or negative. For example, the CC sign for the CI or the transformer windings

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

Related Journal Articles & DOI Links

Selected peer-reviewed publications relevant to 12 Lead ECG Acquisition. Click the DOI to access the full paper (may require institutional access).

Why Choose Us?

Bangalore guidance for robotics, Spectre and autonomous systems projects.