Stepper Motor Drive Matlab

Lubricants: A Review

Logan Jackson1, Victor Boyer2, Tanner Rima3, Edward Cazalas1, *

Abstract

The use of electrical motors and other remote systems are important tools in radiation environments. Certain harsh radiation environments, such as particle accelerators, require the use of remote systems during operation. Stepper motors are one motor, in particular, that have acquired interest in the nuclear field for use in these remote systems. The stepper motor's precision in rotation and holding is a highly desired quality. In this review, the stepper motor is examined for use in radiation environments. The different mechanical parts are introduced and examined from the broader literature of previous work. We attempt to explain the different radiation destructive mechanisms involved with each part of the stepper motor and how the mechanics are affected. Current and past research is explored, identifying either radiation hard alternatives or thresholds of the materials involved, and a general review of stepper motor radiation effects as available in literature.

Figure: System Model & Simulation Flow for Stepper Motor Drive Matlab

1. Introduction

Remote systems are often an important part to work within harsh radiation environments. High radiation fields and high energy particles make it dangerous for direct human intervention in these areas, including in decay radiation fields. Activation via neutron reaction, especially in high energy beamlines, can cause longer lived radiation hazards. Several methods have been developed to minimize dose or prevent exposure all together. These methods have evolved from the primitive ‘reach rod’, to the glove box, to fully remote controllers like the ‘mechanical master/slave manipulator’, and other standard electromechanical devices. The use of these systems, their components, and their radiation tolerance has been a large consideration of research and safety of particular radiation work.

Figure: System Model & Simulation Flow for Stepper Motor Drive Matlab

The stepper motor is an electromechanical device that has been a workhorse, particularly in remote systems. Stepper motors are used in the collimation system of the Large Hadron Collider (LHC) at CERN. The stepper motor excels at high precision and accuracy in movement and positioning. The motor allows for rotation in discreate steps and therefore does not need position feedback in order to maintain a high level of accuracy. These characteristics make it valuable for use in specific radiation environments, including space applications. In general, the stepper motor is quite radiation resistant when excluding the controller systems. Only specific parts have been shown to have significant degradation. These parts include the ball bearing lubricant, the wire coating, and the permanent magnets. Many of these parts already have a limited lifetime due to the normal wear and tear of operation. But this lifetime can be shortened through radiation damage. Throughout this review the individual parts and the stepper motor itself will be examined and evaluated through the work of many different authors.

2. Mechanisms Of Damage

To understand the effects of ionizing radiation on stepper motors, first the damage mechanics must be explored. The effects of radiation damage in a stepper motor can take many forms. In general, the degradation of materials creates malfunctions within specific systems of the motor so therefore, an understanding of radiation damage and radiation interactions must first be understood. There are many different mechanisms and interactions that ionizing radiation has with matter. This is an extensive study, and many textbooks have been written about radiation interactions. Of interest, is how radiation interacts with the target material and what mechanisms are involved in breakdown and change of these materials.

The most fundamental mechanism of radiation damage in materials is Threshold Displacement Energy (TDE) or Direct Displacement Damage (DDD). This is often also referred to as just the ‘displacement energy’. In the simplest terms, this is the minimum recoil energy required for an atom to leave its original location and leave behind a defect in the material. This is typically done via heavy charged particles or neutron interaction. The displaced atom creates a deformity in the crystal structure and therefore weakens the material. This displacement can often result in annealing where the displaced atom finds its original location (or other dislocation site) via diffusion. The displacement can also result in further damage in the creation of large vacancy clusters or vacancy loops from a high rate of dislocations. In these cases, the damage has manifested into a larger chain of damage.

Polymers

Polymers when introduced to radiation can undergo chain scission, causing breakage in polymer chains that can lead to more brittle, less durable plastics. Typically, such radiation induced weakening is irreversible but may require a great deal of radiation exposure to result in the damage, as most polymers are highly resistant to radiation. In a materials review published by Shulman and Ginell, the effects of gamma radiation on certain polymers were found to support this generalization of high resistivity with some notable exceptions. Teflon, as used in stepper motors has a significantly lower tolerance to radiation, experiencing mild to moderate damage at doses around 2 −4 × 104 rad and moderate to severe damage as low as doses greater than 5 × 104 rad. With Teflon being utilized in stepper motors, exposure to radiation dose may over time cause a degradation of the materials and lead to a loss of function. The study states that materials exposed to this level of dose should have limited use, as their functionality may decrease past the doses outlined as severe damage.

Other polymers used in stepper motors such as polyimide and polyamides have significantly higher resistance to radiation damage. White et al performed a radiation robustness experiment on polyamide-imide polymers and found that at doses up to 100 Gy caused no significant decrease in the functionality of the polymer. This level of resistance to radiation is common amongst different classes of polymers and the dose is rather low compared to other studies. In high radiation environments, better performance will be found using thermosetting or condensation polymers from the polyimide-amide groups such as Nylon, Vespel and Kapton.

Metals

Metals, when exposed to radiation, have many of the same interactions that will be discussed with magnets. As the material is exposed to radiation, particle collisions produce a thermal spike of displaced atoms that can transfer energy outwards causing internal damage. Nordlund et al reviewed the current knowledge on radiation damage to several materials and noted that when a metal is introduced to radiation, the thermal spike acts nearly like a thermodynamic system with a Maxwell-Boltzmann like energy distribution. Much of the initial damage produced by radiation is mitigated by recrystallization, however some of the produced damage remains inside the metal. Small defects produced by these cascades can result in damage that can cause corrosion, embrittlement and acceleration of oxide formation within the metals. Additionally, metal atoms can undergo transmutation via neutron reaction. This may lead to changes in the chemical state of the atoms as it decays and lead to a less stable structure of the metal materials.

3. Stepper Motor Materials And Construction

In understanding how the stepper motor is affected by radiation it is first important to understand how the motor works and the different parts involved. Stepper motors operate by splitting the rotation of the motor into individual steps. There are three different kinds of stepper motors available. Variable reluctance, permanent magnet, and hybrid. All three utilize a similar method of operation, but we will be focusing on hybrid stepper motors. Hybrid stepper motors follow a NEMA # sizing characterization, where the number designates the side length of the motor face multiplied by 10.

1

An electric pulse is fed into the motor, energizing the coils and causing the rotor teeth to align with the stator teeth. This advances the rotor one step. A new pulse energizes the next set of stator teeth, and the rotor advances an additional step. A visual portrayal of this can be seen in Figure 1. The most common step size is 1.8°. Due to this, one pulse gives 1.8° or rotation, 10 pulses rotates 18°, and 100 pulses rotates 180°. Continuous rotation is achieved by supplying the electric pulses at a specific frequency. Increasing the frequency results in faster rotation and decreasing the frequency results in slower rotation. Because of this, stepper motors offer very precise rotation control and high torque holding characteristics.

Stepper motors are constructed by placing a magnetic disk between two rotors on the rotor shaft. This rotor assembly is suspended by two bearings on the front and rear faces. Both front and rear faces are attached to the stator, which encircles the rotor assembly. The magnetic field produced by the copper windings on the stator is what makes the rotor turn. Figure 2 shows an uncoiled schematic of the different stepper motor parts and their location in construction.

1 Reprinted from IET Power Electronics, Vol 13 / Issue 11, Jae Wook Jeon, Kien Minh Le, Hung Quang Cao, et al, ‘Improving the accuracy of permanent magnet rotor position estimation for stepper motors using magnetic induction and harmonic rejection’. Copyright (2020), with permission from John Wiley & Sons.

Figure 1 - Image of stepper motor windings and permanent magnet. A and B indicate windings that are energized together. The rotor has a magnet of alternating North and South pole facing teeth, allowing for smaller step sizes within the motor.

The ball bearings used in stepper motors are deep groove ball bearings, typically made up of 52100 chrome steel. Approximately 85% of ball bearings use a grease lubricant that follows these proportions: 85% mineral oil, 10% thickener, and 5% other additives. The thickener is frequently lithium stearate, but can also be calcium, aluminum, and polyurea based. The amount of grease contained within the bearing falls between 25% and 35% of the internal volume.

Dimensions and approximate grease volumes are listed in inches and millimeters in Error! Reference source not found.. The front and rear motor faces are typically made from aluminum. These support the rotor assembly. The shaft is made of mild steel, and the rotor and stator are made of silicone steel laminations (Fe: 19%, Ni: 78%, Si: 3%).

2

2 Moons’, “Step Motor – Basic Structure & Operation.” Accessed: Jun. 23, 2025. [Online]. Available: https://www.moonsindustries.com/article/basic-structure-and-operating-principle-of-stepper-motor.

Citation:

Table 1 - Ball Bearing Dimension and Grease Volume

10.65 Ml

Figure 2 - Uncoiled image of stepper motor parts. The stator windings are composed of copper wire (Cu: 99.3%, remainder: O) with an insulative coating approximately 0.0010 in. thick. The common kinds of insulation, organized by temperature ratings, are 105°C: formvar (vinyl-acetal film), 155°C: polyurethane, 200°C: polyamide imide, 240°C: polyimide, 260°C: Nylon/Teflon.

4. Radiation Sensitive Parts Of Electrical Motors

Many of the materials of stepper motors are quite resistant to radiation. All materials will break down in some capacity, but mostly due to mechanical effort. There have been few studies on the radiation effects of whole electromagnetic motors in an attempt to classify operation thresholds for these motors. Discussion on the whole motor behavior is presented, but focus will be given to individual parts within the system and how these parts are affected in radiation environments.

These radiation sensitive parts, likely to affect the overall lifetime of the motor, will be discussed throughout. First it is important to mention that many of the electrical components included in the motor controller and driver are extremely sensitive to radiation and are only briefly discussed within this review. These components include semiconductor devices often seen in computer systems.

Because of the particular sensitivity of most computer electronics, these systems are often placed far away from the radiation environment and connection is preserved through long wires. Further discussion of these systems and their possible difficulties resides in Section 5.

The first notable radiation sensitive part is the ball bearing lubricant. This being a typically organic material, it is very susceptible to degradation. Without proper lubrication characteristics, the motor bearings will experience increased friction when rotating. This causes wear on the bearing balls and ultimately, this wear could cause inconsistencies in rotation or vibrations affecting overall precision of the device. A possible alternative to standard stainless steel with lubrication bearing is a non-lubricated ceramic bearing. The alternative use of non-lubricated bearings is discussed in Section 9.

Wires are another notably susceptible part of the stepper motor. Wires are coated in insulating materials to improve their overall conducting/insulating properties by reducing the impact of interference from other close by wires. Insulation is a non-conductive material such as polyethylene or rubber. The insulation material of the wires can see significant degradation which can lead to interference and an increase in wire resistance. A more in-depth analysis is presented in Section 7.

Another notably sensitive part is the permanent magnet. Although there are not many studies on magnets taken straight from stepper motors, there are studies involving equivalent magnets of the same materials and strengths. Radiation exposure can cause decreases in the magnetic field of a magnet. Further explanation of the different magnets and how they behave is described in Section 6. This decrease can directly affect the mechanical output of the stepper motor in decreased torque and holding torque.

5. Radiation Effects On Motor Systems

Ionizing radiation primarily affects electric motors through two means: material degradation and electronic component interference. These effects occur from buildup of radiation dose over time and rarely have any immediate consequences. However, prolonged exposure and dose buildup can create performance decreases in stepper motors. The areas of greatest concern are the breakdown of electrical insulating coatings, weakening magnetic field strength, and breakdown of lubricants.

Previous studies have shown the effects of radiation on motor components, but extensive work has not been done on stepper motors specifically. Based on related works it is expected that a substantial decrease in magnetic field strength, breakdown of lubricant, and increase in wire resistance due to insulation breakdown will result in an overall decrease in performance. , , , , These performance decreases would manifest in lower torque output and therefore RPMs in the motor.

These performance decreases have been seen in DC servo motors under gamma irradiations performed by Oak Ridge National Lab. The DC servo motors were exposed during acceleration and deceleration cycles with radiation exposures of 2 −3𝑥109 𝑅 before failure. The failures were attributed to shortages in the motor windings. AC servo motors and stepper motors were also tested in this study. For both motors, no decrease in performance was observed up to 109 𝑅. The stepper motor in particular had been built and tested to 108 𝑅. After testing, an examination of the parts showed no serious degradation of individual parts. Further and extended research is needed to determine the operation thresholds of stepper motors in radiation fields. Based on the performance degradation of the DC motor, a shortage in the wire windings might be the first indication of performance degradation in stepper motors.

Another system that must be considered with the uses of stepper motors in high radiation environments are the controls. The controls consist of controllers and drivers that are used to power and manipulate the motor. The electronics involved in the motor drive, controller, and power systems of the stepper motor are particularly sensitive to radiation which include most modern semiconductors devices. , , , Because of this, these controls must either be shielded or removed from the environment entirely. Controller systems like the ones used with the collimators in the Large Hadron Collider at CERN prevent irradiation of the controllers and drivers by keeping them in radiation free areas and connecting the motors through long wires. Feedback positioning controls like position sensors must also be considered along with these other electronics. These position sensors provided verification of completed rotations.

During normal operation or due to wear caused by it, the motor can experience malfunctions were the motor fails to complete full step rotations. When this happens, the motor and the controller will be misaligned, and the position of the motor will not be true to the controls. This presents its own set of challenges to verify complete accuracy of the motor in environments where a position sensor within the motor cannot be sustained. Several authors have done research to improve the positioning accuracy and controls of the stepper motors used in radiation environments using open loop systems or other methods. Another method might involve the use of shielding to protect the whole motor, controls, and sensors. It is important to protect these sensitive electronics when implementing stepper motors in radiation environments.

Neutrons

Radiation effects on magnets have been the focus of numerous studies to ascertain the extent of demagnetization caused by the radiation. Previous studies have concluded that it is likely that radiation dose can cause thermal spikes within the materials that then lead to displacement cascades. These thermal spikes, typically of nanometer or larger scale radius will then allow for domain reversals leading to localized demagnetization. This effect is particularly noted in NdFeB permanent magnets where it displays a noticeable flux dependency. Cost et al. investigated the effects of fast neutrons on such magnets. When irradiated with a fluence of order of magnitude ~1𝑥1015 N/cm2, it was found that after a full irradiation, magnets at 350K experienced nearly a 60% reduction in remanence and magnets at 426 K experienced an even greater decay at nearly a 95% loss in remanence post irradiation. Significantly, the authors explained that when tested for potential annealing effects, for up to 4.25 hours there were no long-term effects in the remanence and that the effects of the irradiation are reversible. Their explanation of the temperature dependence on the degree of demagnetization was the proximity to the Curie temperature causing an increased likelihood of the displacement cascades to nucleate new reversal domains.

It has been noted that past the threshold of fluences near 1016 neutrons/cm2, NdFeB magnets receive permanent structural damage due to heat and annealing effects which disallow full recovery of magnetism. Cost et al. further determines that non-annealing decay in remanence allows for full recovery of magnetism, and due to pinning in the domain walls from the radiation process, would pin domain walls increasing the coercivity by up to 20% from the radiation.

Klaffy and coworkers studied the effects of thermal neutrons on NdFeB magnets, hypothesizing a heightened decay in remanence due to the 3837 b (barns) absorption cross section of 10𝐵(𝑛,  𝛼)7 𝐿𝑖 , releasing an alpha particle that can induce thermal spikes within the magnet itself. By incorporating the thermal spike model, they found that this thermal spike could approach or exceed the curie temperature of the magnet, reversing the domains. They concluded that the alpha particles emitted during the Boron capture of a thermal neutron played a significant role in the demagnetizing process.

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.

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).

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.

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).

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.

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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