Resonant Wireless Charging Matlab

1

Suppressing Leakage Magnetic Field in Wireless Power

Transfer Using Halbach Array-Based Resonators

Abstract—Wireless power transfer has the potential to seamlessly power electronic systems, such as electric vehicles, industrial robots, and mobile devices. However, the leakage magnetic field is a critical bottleneck that limits the transferable power level, and heavy ferromagnetic shields are needed for transferring large amounts of power. In this paper, we propose a ferrite-less coil design that generates an asymmetric magnetic field pattern focused on one side of the resonator, which effectively reduces the leakage magnetic field. The key to enabling the asymmetric field pattern is a coil winding strategy inspired by the Halbach array, a permanent magnet arrangement, which is then tailored for wireless power using an evolutionary strategy algorithm. Numerical analyses and simulations demonstrated that the proposed coil structure delivers the same amount of power as spiral coils, while achieving an 86.6% reduction in magnetic field intensity at a plane located 75 mm away from the resonator pair and a power efficiency of 96.0%. We verified our approach by measuring the power efficiency and magnetic field intensity of a test wireless power system operating at 6.78 MHz. These findings indicate that our approach can efficiently deliver over 50 times more power without increasing magnetic field exposure, making it a promising solution for high-power wireless power transfer applications.

Figure: System Model & Simulation Flow for Resonant Wireless Charging Matlab

Index Terms—Wireless power transfer, leakage magnetic field, Halbach array.

W

IRELESS power transfer via magnetic field can seamlessly empower various electronics, but the leakage magnetic fields generated by these systems can cause negative effects, such as tissue heating and electromagnetic interference, which pose critical limita- tions on the transferable power level and application scenarios .

Figure: System Model & Simulation Flow for Resonant Wireless Charging Matlab

Ferromagnetic shields have been used to suppress those fields , but they are heavy and expensive and become lossy at frequencies exceeding a few MHz , . Therefore, there is a need for a resonator design that can suppress leakage magnetic fields without using ferromagnetic material and can also efficiently transfer power, especially for mobile applications where weight and cost are critical factors.

To address this need, we propose a ferrite-less resonator structure that generates an asymmetric magnetic field pattern focused on a single side of the resonator. This design enables efficient wireless power transfer and leakage magnetic field suppression, with the key feature being a parametrically optimized coil pattern that vertically arranges numerous helix and spiral coils wound in both the clockwise and counterclockwise directions. This winding generates a magnetic field pattern analogous to the Halbach array, an arrangement of This work was partially supported by JST ACT-X Grant Number JPM- JAX190F, JSPS KAKENHI Grant Number 23H03378, and Value Exchange Engineering, a joint research project between Mercari, Inc. and the RIISE.

The authors are with the Graduate School of Engineering, The Univer- including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

This is the accepted version of the manuscript. The final version is available

Suppress

Fig. 1. Suppressing the leakage magnetic field using a resonator structure inspired by the Halbach array. (a) A Halbach array composed of five permanent magnets. The magnetic field on one side is enhanced, while it is suppressed on the other side. (b) Suppressing the leakage magnetic field using resonators inspired by Halbach arrays.

permanent magnets that focuses the magnetic field to a single side of the array (see Fig. 1). While prior literature has described coil structures and a ferrite shield structure inspired by the Halbach array, the presented coil designs can not simultaneously achieve field suppression and high-efficiency power transfer because these simple imitations disregard critical factors, such as power losses and the difference in field distributions between coils and permanent magnets. To overcome this limitation, we used the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) algorithm to optimize the coil pattern for two design priorities: (a) leakage magnetic field sup- pression and (b) high power transfer efficiency. We also demonstrated how varying the weights of these two design priorities can affect the performance of the resonators, and these results were verified through Method of Moments (MoM)-based simulations. Finally, we built a wireless power transfer test system operating at 6.78 MHz and measured the leakage magnetic fields to confirm the results.

Ii. Halbach Array-Based Resonator

The Halbach array is an arrangement of permanent magnets, first proposed in 1973, which enhances the magnetic field of one side of the array, while suppressing the field on the other side , (See Fig. 1(a)). On the top side, the N and S poles of adjacent unit permanent magnets are clustered, virtually forming a large magnet that generates a far-reaching magnetic field. Conversely, the N and S poles are isolated on the bottom side and behave as small magnets that generate a quickly decaying magnetic field. Combined together, this makes the magnetic field focused on one side and suppressed on the other side of the magnet.

For application to wireless power, the permanent magnets need to be replaced with inductors that form an oscillating magnetic field, and a field analogous to the Halbach array can be composed by combining helix and spiral coils with various polarities . We can observe from the cross-section of axis-symmetric coils that helix coils can imitate vertical magnets, and the spiral coils can imitate horizontal magnets (See Fig. 2(a)). By connecting these helix and spiral coils in the correct polarity, we can form a resonator that generates a field analogous to the Halbach array (See Fig. 2(b)(c)(d)).

+

Fig. 2. Structure of the Halbach array-based resonator. (a) Replacing the permanent magnets of the Halbach array with helix and spiral coils. When the coils are combined, the magnetic field is enhanced on the upper side and suppressed on the lower side. (b) Parameterization of the Halbach array-based resonator. ri are the radii of each coil, ni are the number of turns of each coil, and h is the height of the resonator. (c) The Halbach array-based resonator with all helix and spiral coils configured. This structure is a series connection of five helices and spiral coils with capacitors inserted in series. (d) The position of the transmitter, receiver, and measurement plane, in which the magnetic field is measured. g is the distance between the resonators, and hm is the distance from the resonators to the measurement plane.

Iii. Optimization Method Using An Evolution Strategy

While it is possible to conceptually mimic the magnetic field distribution of a Halbach array using the coil structure outlined in section II, a straightforward design based on this concept may not be adequate to achieve high performance in wireless power systems.

Several critical factors for wireless power, such as power loss, are not considered, and the original Halbach array premises a 1-D array of square-shaped magnets rather than an axis-symmetric structure. The field leakage at the array edges is significant, and the magnetic field distribution of coils and permanent magnets is different. These issues are interdependent and challenging to address empirically. Therefore, we proposed incorporating an evolution strategy algorithm in the design process. A parameterized structure, an evaluation function, and an optimization algorithm are required to design a structure using an optimization algorithm.

Fig. 2(b) shows the parameterization of the coil structure. The coil comprises three helical coils and two spiral coils, encoded as a twelve-element vector⃗a = {⃗r,⃗n, h}. This vector includes the radius vector⃗r = {r1, r2a, r2b, r3a, r3b, r4}, the number of turns vector⃗n = {n1, n2, n3, n4, n5}, and the height h (scalar). Note that the outer helical coil’s radius is fixed to rcoil, and the spiral coils (coils 2 and 3) have two radii, i.e., inner and outer radii. To ensure physical validity and prevent interference, we imposed the following restrictions on the geometry: the radii were bounded by r1 < r4 < rcoil and ria < rib < rcoil (i = 2, 3); the height was set within 5 mm< h <100 mm; and the lower bounds of r1, r2a, and r3a were set to 3 mm. The radius of the entire coil rcoil was fixed at 150 mm, and the number of turns ni was restricted to integers between 0 and 5.

Secondly, the evaluation function was tailored to the specific requirements of the application, which for this study were (a) minimizing the leakage magnetic field and (b) maximizing power transmission efficiency. To this end, we defined the evaluation func- tion E as a weighted sum of two factors: the maximum magnetic field intensity on a measuring plane Hmax (as shown in Fig.2 (d)) and the maximum power transfer efficiency ηmax. The evaluation

(1)

Here, E is to be minimized during the design process, and w is a weighting factor determined based on the application’s requirements. In the optimization process, we calculated Hmax and ηmax using numerical analysis because performing electromagnetic field simula- tions is time-consuming and limits the feasible number of function evaluations. We defined efficiency as the maximum efficiency ηmax obtained when the load value is tuned to the value that maximizes

20 Mm

power transfer efficiency, assuming the maximum efficiency point tracking technologies developed in previous studies . We calculated ηmax based on the mutual inductance M and the copper losses of the two resonators r1, r2, where we computed M using Neumann’s formula and the copper losses by multiplying the wire length by the wire resistance of a unit length, considering the skin effect .

Hmax was the maximum magnetic field intensity in a measuring plane hm downward from the top of the transmitter, as shown in Fig. 2(d). As this field intensity depends on the operating conditions, we calculated it for a power delivery of 1 W to the load using Biot- Savart’s law.

Finally, the optimization algorithm was selected based on the properties of the input parameters and the evaluation function. For this study, the input parameters were a mix of real numbers (radii, height) and integers (number of turns), and the computation of Hmax required the selection of maximum value, which made the function non- differentiable. Therefore, we used the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) –, which is known to be efficient and converge quickly under such conditions.

Iv. Optimization And Simulation Results

We conducted the optimization process by varying the weight w and plotted the resulting power transfer efficiency and leakage magnetic field in Fig. 3. To obtain these results, we iterated the optimization ten times with a limit of 10,000 function evaluations for each case and plotted the smallest value. The parameters used for this evaluation are listed in Table I. Each optimization converged after approximately 2,000 function evaluations. The figure demonstrates that a larger weight w places more emphasis on reducing the leakage magnetic field, resulting in lower efficiency, and vice versa for a smaller w.

Next, we further investigated the optimized resonator structure and compared it with previous designs by conducting electromagnetic simulations using the method of moments (MoM) simulations in FEKO. As for the proposed design, we used the optimized design resulting from parameters (w, hm) = (0.3, 75 mm) and compared

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

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.