Ferrite Permanent Magnet Research Articles

Study of the magnetic and structural properties of BaFe12 – xCuxO19 ferrites obtained by hydrothermal synthesis

Hexagonal ferrites of M-type (in particular, BaFe12O19) are magnetic materials with functional characteristics affected both by chemical composition and technology of their synthesis. We present the results of studying the magnetic and structural properties of BaFe12 – xCuxO19 hexaferrites (x = 0, 0.1, 0.2, 0.3, 0.4) obtained by hydrothermal synthesis with partial substitution of copper for iron. The composition of the synthesized samples was analyzed using X-ray diffraction, and the magnetic characteristics were measured using a vibration magnetometer. It has been revealed that the coercivity of the ferrite powders depends non-monotonically on the copper concentration and reaches the maximum (5629 Oe) and minimum (4698 Oe) values at x = 0 and x = 0.2. The presence of copper reduces the coercive force, but at the same time the values remain rather high compared to the results of similar studies. The saturation magnetization of the obtained ferrites gradually decreases (from 65.88 to 60.75 A · m2/kg at x = 0 and x = 0.4, respectively) with increasing. The distribution of Cu over ferrite sublattices was studied using Mössbauer spectroscopy. It is shown that in the hexaferrite structure, copper ions preferentially occupy 12k and 4f1 sites. Hence, a decrease in the saturation magnetization with increasing x is most likely attributed to the presence of side non-magnetic phases observed on X-ray diffraction patterns. It is also revealed that during synthesis, copper participates in the formation of low-melting phases on the surface of hexaferrite grains which promotes agglomeration of the particles. Thus, the resulting powders can potentially be sintered at lower temperatures and, therefore, without a significant increase in the size of crystallites. Herewith, the coercivity retains its original high values. The results obtained can be used in developing ferrite permanent magnets with improved characteristics.

4D printing of the ferrite permanent magnet BaFe12O19 and its intelligent shape memory effect

4D printing of the barium ferrite permanent magnets provides new opportunities for intelligent structure and process innovation of permanent magnets. In this paper, the preparation, filament manufacture, and intelligent printing methods with shape memory/recovery effect are studied for the barium ferrite permanent magnet. Firstly, the PLA/TPU/BaFe12O19 composite materials are developed by adding different contents of ferrite permanent magnet BaFe12O19 powders into the PLA/TPU (polylactic acid/thermoplastic polyurethane) matrix. The weight percentage of the BaFe12O19 is 10–40 wt% with an interval of 10 wt%. Secondly, the composites are pelletized and further extruded to manufacture composite filaments with different BaFe12O19 contents. Scanning electron microscope (SEM) is used for the microstructural analysis. The BaFe12O19 particles are uniformly distributed in the PLA/TPU matrix, and the slight particle agglomeration phenomenon occurs in the composite filaments with 30 and 40 wt% BaFe12O19. The thermal properties of PLA/TPU/BaFe12O19 composite filaments are analyzed by thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC). After adding the barium ferrite particles, the glass transition temperature of the composite filaments changes within a small range from 53.5 °C to 55 °C. Thirdly, the filaments are successfully manufactured to magnet parts by the fused deposition modeling (FDM) 3D printing for the tests of mechanical, magnetic, and shape recovery properties. With the increase of the barium ferrite content, the magnetic properties show a rising trend, proving the feasibility of using 3D printing technology to make magnets. The shape memory effects of the printed parts are excellent and the shape recovery ratios show a rising trend, from 85.6 % to 88.9 % under heat contact stimulus and from 88.9 % to 97.8 % under electromagnetic induction non-contact stimulus. Relatively, the parts hold fast response speed due to direct contact with the heat source under the heat stimulus, and the parts hold higher shape recovery ratios due to more heats produced under the electromagnetic induction stimulus. The addition of magnetic particles is helpful to improve the heat transfer ability and provide the possibility of non-contact heat transfer. The magnetic parts with complex structure and intelligent shape memory/recovery effect can be achieved for special application requirements. As a result, the research of this paper expands preparation methods of new magnetic composite materials, explores the manufacture process for intelligent magnets and lays a solid foundation for the development of new permanent magnet devices.

Two-Stage Optimal Design of Concentric Ferrite PM Layer IPMSM for Micro-EV Traction Considering Driving Characteristics

Two-Stage Optimal Design of Concentric Ferrite PM Layer IPMSM for Micro-EV Traction Considering Driving Characteristics

Investigation of shaded pole stator topology for low power AC motors design

PurposeThis paper aims to investigate the features of single phase shaded pole stator with squirrel–cage rotor or permanent magnet rotor, that leads to an investigation of these topoloties as induction motor or synchronous motor. The comparative analysis is realised for the following three topologies: single phase shaded pole induction motor (SPIM) with squirrel–cage rotor, the second topology (single phase synchronous motor) has the same stator configuration but with permanent magnet rotor and the third investigated topology is similar to the second one, where the stator poles instead of iron steel are made of soft composite material.Design/methodology/approachThe investigation in this work starts with a performance analysis of single-phase SPIM. Afterwards for the same stator topology the squirrel rotor is replaced with a two-pole permanent magnet rotor and the same performance analysis is realised for this topology. Finally, the second topology is improved bay replacing the iron steel stator poles with stator poles made of soft magnetic composite material and performance analysis is realised for this third type of topology as well. The performance analysis of all topologies is realised by implementation of finite element method and finite element analysis.FindingsThe presented data and diagrams from the realized investigation show that single phase synchronous motor with shaded pole stator has an improved characteristics in comparison with the initial single-phase SPIM. Finally, the third topology realized on the bases of the single-phase synchronous motor has the best performance characteristics due to the implementation of soft magnetic material in the realization of the stator poles. The proposed methodology for structural and performance improvement of a single-phase SPIM topology opens the possibility for additive manufacturing application and significant cost reduction.Originality/valueThe focus was put on exploration the possibilities of the single-phase shaded pole stator topology for application in low-power and low-cost single phase self-starting motors. By simple replacement of the squirrel–cage rotor, in the reference AKO-16 motor, with one-piece ferrite permanent magnet rotor, the self-starting single phase synchronous motor was derived. In the next step, owing to simplify the SPPM motor production process and manufacturing, the stator poles instead of iron steel lamination were made of soft composite material Somaloy®. It opens the possibility for additive manufacturing application and significant cost reduction.

Calcination temperature effect on formability and magnetic properties enhancement of anisotropic Ca-La-Co substituted M-Type Sr-hexaferrites permanent magnets

In this study, Ca-La-Co substituted M-type Sr-Hexaferrites (Ca0.35La0.47Sr0.18Fe10.87Co0.22O19-δ) were prepared via conventional solid-state reaction, with the calcination temperature ranging from 1240℃ to 1290℃. The grain size of the calcined powder increased with the elevation of calcination temperature, and XRD characterization confirmed the formation of Sr-hexaferrite structure at higher temperatures. SEM analysis revealed hexagonal grain morphologies in the calcined samples. Additionally, the microstructure of the fine-milled magnetic powder transitioned from ultrafine particles to larger plate-like granules as the calcination temperature increased. Remarkably, the remanence (Br) showed an upward trend with increasing calcination temperature, peaking at 4571 Gauss, while the intrinsic coercivity (iHc) reached an optimized value of 5306 Oe at 1280℃. Notably, the formability of M-type Sr-hexaferrites was influenced by the calcination temperature, with the sintering radial shrinkage rate (Sh-D) being <12 % and the required molding pressure of magnetic powder being <500 kg/cm2, both contributing to improved yield and cost-effectiveness in ferrite permanent magnet production. These findings effectively address previous challenges associated with achieving high characteristics and formability, leading to comprehensive enhancements in magnetic properties, operability, and production efficiency. The anisotropic Ca-La-Co substituted M-Type Sr-hexaferrites permanent magnets produced in this study emerge as promising candidates for high-performance rare-earth-free permanent magnets, particularly showcasing the optimal effects achieved at the calcination temperature of 1280℃.

Evaluating the potential white shark (Carcharodon carcharias) swim pattern manipulation capabilities of the novel and noninvasive Shark Exclusion Barrier

Abstract Even though the risk of a negative encounter with a large and potentially dangerous shark species (e.g. white sharks—Carcharodon carcharias) is exceedingly rare, some localities implement indiscriminate shark culls to minimize this risk. Due to the negative ecological impact that these lethal shark control measures can have, the present study aimed to test a novel and eco‐friendly shark barrier system, known as the Shark Exclusion Barrier. The Shark Exclusion Barrier is a shark deterrent technology that is composed of a combination of interconnected and telescoping vertical barrier elements (i.e. the visual stimulus) and electromagnetic stimuli (e.g. electromagnets and Barium Ferrite (BaFe12O19) permanent magnets). Using this system, two separate C. carcharias swim pattern manipulation studies were conducted over the course of two research seasons. In the first season (i.e. 2021), 9, 1‐h trials were conducted where 9–13 different C. carcharias interacted with the barrier. In the second season (i.e. 2023), 35, 2‐h trials were conducted where 6–10 C. carcharias interacted with the barrier. Throughout experimentation, C. carcharias exhibited a significantly greater entrance frequency (p &lt; 0.05) and a significantly reduced pass around frequency (p &lt; 0.05) towards the control region when compared to the Shark Exclusion Barrier region. Furthermore, the barrier exhibited the ability to maintain its structural integrity during swells of ≥2.13 m, breaking waves of ≥1.52 m and a current of ≥1.12 m/s. Due to the promising results, this technology warrants further investigation to determine if it is a plausible alternative to lethal culling measures.

Designing and Prototyping an Axial-Flux Machine Using Ferrite PM and Round Wire for Traction Applications: Comparison With a Radial-Flux Machine Using Nd-Fe-B PM and Rectangular Wire

Designing and Prototyping an Axial-Flux Machine Using Ferrite PM and Round Wire for Traction Applications: Comparison With a Radial-Flux Machine Using Nd-Fe-B PM and Rectangular Wire

Study on Performance Improvement through Reducing Axial Force of Ferrite Double-Layer Spoke-Type Permanent Magnet Synchronous Motor with Core Skew

Recently, due to the price fluctuation and supply instability of rare earth mineral resources, there has been a lot of development of electric motors using non-rare-earth permanent magnets. As a result, motors using Dy-free permanent magnets and ferrite permanent magnets are being researched, and, in particular, ferrite permanent magnets often utilize spoke-type structures, which are magnetic flux concentrators, to compensate for their low coercivity and residual flux density. However, in general, spoke-type PMSMs do not use much reluctance torque, so double-layer spoke-type PMSMs have been studied for their more efficient design. Unlike general spoke-type PMSMs, double-layer spoke-type PMSMs can utilize high reluctance torque by increasing the difference between d-axis and q-axis reluctance. However, as the difference in magnetic resistance increases, vibration and noise are generated, which adversely affects the mechanical part and shortens the life of the motor. Although this problem seemed to be solved by applying core skew in the previous study, it was confirmed that the axial force caused by the axial leakage flux occurred in the maximum torque per ampere (MTPA) control section and the torque ripple was increased. Therefore, in this paper, a model that can apply symmetrical core skew and reduce axial force is proposed. First, the causes of the axial force generated in previous studies were analyzed. Based on the analysis of these causes, a new symmetrical core skew structure was proposed, and its justification was verified through FEA.

Surface magnetic flux density optimization considering effect of aligned magnetic field molding conditions of ring-shaped multi-pole anisotropic ferrite permanent magnet for DC motors

The ring-shaped anisotropic ferrite magnet with multiple poles boasts significant benefits for brushless DC motors (BDCMs). However, the prevalent production method involves dry magnetic field molding, making it challenging to enhance the magnetic properties. Herein, ferrite powder made from iron oxide, a by-product of the steel industry, is used as the starting material of magnets, and the differences between dry and wet molding approaches on the surface magnetic flux density of a ring-shaped multi-pole anisotropic ferrite magnet are first investigated. ANSYS MAXWELL conducted an initial simulation to achieve the design specifications of the wet molding mold. Following this, the mold was prepared for the fabrication of ring magnets. Compared to magnets prepared via dry molding, those produced through wet molding exhibit a peak surface magnetic flux density of approximately 15.9% higher, demonstrating significant potential for industrial applications and substantial enhancement of the key magnetic properties of wet molded ferrite ring magnets. To achieve increased surface flux density of ring magnets, it is common practice to utilize magnetic powders with greater magnetic properties when molding the magnets. However, this requires a costly mold redesign. In this study, higher surface magnetic flux densities can be achieved for ring magnets by simply adjusting the shape, size and magnetization direction of NdFeB permanent magnets that provide a constant aligned magnetic field in the mold without requiring any alterations to the existing mold's dimensions. The findings of this study could improve the effectiveness of existing motor designs. The usage of ring-shaped multi-pole anisotropic ferrite magnets is anticipated to witness a surge in the coming years, driven by the growth of energy-efficient motors in diverse sectors.

Demagnetization analysis of outer-rotor-type BLDC motors considering permanent magnet overhang structure

This paper presents an analysis of demagnetization of an outer rotor type brushless DC (BLDC) motor with a permanent magnet (PM) overhang structure. The proposed model converts the operating points of PM to consider such a three-dimensional (3D) structure in two dimensions (2D). In addition, the rotor yoke thickness of the proposed model is increased to consider the housing rotor. Ferrite PMs require demagnetization analysis owing to their decreasing coercivity at lower temperatures compared with rare-earth PMs. Hence, demagnetization analysis is conducted using a proposed model while considering, the PM overhang structure. The demagnetization analysis results are compared with the results of proposed model and 3D FEA analyses.

Sintering temperature optimization for enhanced magnetic performance in La–Ca–Co doped strontium ferrite

The effectiveness of employing La-Ca-Co co-doping has been demonstrated as the optimal approach for enhancing the magnetic performance of strontium ferrite. However, limited studies have explored the evolution of the magnetoplumbite phase and its correlation with the sintering temperature. In our research, La-Ca-Co doped strontium ferrite permanent magnets were fabricated using a conventional ceramic process and a two-step sintering technique. After sintering at different temperatures, all the samples possess proper c-axis orientation. When the sintering temperature was raised from 1175 °C to 1205 °C, there was an upward trend observed in the remanence Br, increasing from 430 mT to 439 mT. The coercivity Hcj exhibited an increase from 380 kA/m and reached its peak at 397 kA/m at 1185 °C. Although the Br value remained favorable, the coercivity experienced substantial deterioration, reaching its lowest point at 303 kA/m at 1205 °C. Under a sintering temperature of 1195 oC, magnetic performance with optimal energy product was achieved, with Br of 439 mT, Hcj of 379 kA/m, Hcb of 318 kA/m, and (BH)max of 35.5 kJm-3.

Improved calculation of core losses of high-speed motors with two different permanent magnets considering higher order current harmonics

In high-speed permanent magnet synchronous motor drives, time harmonics in the current occur owing to the carrier frequency of the inverter, which affects the core losses among the electromagnetic losses. According to Steinmetz’s equation, the core loss depends on the frequency and magnetic flux density, with each term influenced by harmonic currents. Therefore, to accurately predict core loss, it is necessary to consider harmonic currents. This study presents the effects of differences in the resistance, inductance, switching frequency, and harmonic current on the core loss for two models with different PMs at the same output power. Core losses are significantly affected by harmonic current content and magnetic field behavior, making the analysis of harmonic components and magnetic field behavior essential. To achieve this, the stator core was divided into segments to examine the magnetic field behavior owing to harmonic currents in each region, thus facilitating a comprehensive analysis of the core losses. When the results were compared with the experimental data, it was observed that the analysis of harmonic currents significantly improved the accuracy compared to the analysis based solely on sinusoidal currents; in particular, the error rate reduced from 37.8% to 4.1%. Furthermore, it was confirmed that ferrite PMs resulted in smaller core losses owing to harmonic currents than rare-earth PMs. This finding suggests that ferrite PMs are a suitable alternative to high-speed permanent-magnet synchronous motors.

Design and analysis of a hybrid permanent magnet variable leakage flux motor for low core loss and wide speed range

In this paper, a new hybrid permanent magnet variable leakage flux (VLF-HPM) motor is proposed. In order to enhance motor speed range, short arc-shaped and elliptical-shaped magnetic barriers are placed on the q-axis magnet circuit, realizing the so-called leakage flux effect. In addition, ferrite PMs are artfully designed, so self-leakage flux can be reduced while main flux is enhanced. The relationship among PM topology, flux barrier and flux-regulation capability are also investigated in detail. Finally, the electromagnetic performance of VLF-HPM motor is evaluated by the finite element analysis and compared with a conventional V-typed PM motor. It is noted that, compared with conventional V-typed PM motor, the VLF-HPM motor possesses lower core losses and a wider speed range, which offers a new research path for high-performance PM motor.

Magnetic Coupling Effect and Performance Analysis of Dual Rotor Permanent Magnet Flux Switching Generator for Counter Rotating Wind Power Generation

To eliminate slip rings, brushes, and terminate gear-box mechanism, ferrite permanent magnet (PM) based counter rotating dual rotor PM flux switching generator (CRDRPMFSG) for direct drive counter rotating wind turbine (D <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> CRWT) application is proposed in this paper. Initially, the mechanism of gearless and brushless counter rotating wind power generation is discussed, and a simplified formulation opted for the slot/pole combinations. The proposed CRDRPMFSG encapsulate inner and outer machines with circumferentially magnetized PM enclosed by non-overlapped armature windings; thus, offering reduced overhang with compact design. However, co-axially linking the inner and outer machines through a shared stator yoke results in serious issues of magnetic coupling due to dual air-gap fields. To this end, eight topologies with various slot/pole combinations are comprehensively investigated using finite element analysis (FEA) for magnetic coupling effects and its influence on electromagnetic performance. From the analysis, it is shown that magnetic coupling level influence electromagnetic performance i.e., average torque, ripple rate, power factor, efficiency, losses, and output power. Moreover, it is noted that coupling level can be reduced by adopting same stator teeth in inner and outer machines or same stator teeth with different rotor poles. Finally, the predicted FEA calculations are verified experimentally with four benchmarked CRDRPMFSG prototypes.

Torque Ripple and Mass Comparison between 20 MW Rare-Earth and Ferrite Permanent Magnet Wind Generators

This article investigates the comparison between two configurations of 20 MW offshore synchronous wind generators using ferrite and rare-earth permanent magnets. The optimization-based comparison concerns the torque ripple and active mass, which are two crucial criteria for offshore wind generators. Both generators adopt surface-mounted permanent magnet type with direct-drive technology to avoid problems associated with the gearboxes. The result shows that at the full-load condition, the ferrite permanent magnet generator can reduce the torque ripple to as much as 0.12%, while the rare-earth counterpart can be about 2.5 times lighter than the former one.

Comparative Study of Mechanical and Electrical Characteristics of High-Strength and Conventional Electrical Steel for EV Traction High-Speed Multilayer IPMSM Using Rare-Earth Free PM

In this article, the electrical and mechanical characteristics of multilayer interior permanent magnet synchronous motors (ML-IPMSMs) using ferrite permanent magnets (PMs) are compared when driven at high speeds with respect to the type of electrical steel. In high-speed operation, the mechanical and electrical characteristics of ML-IPMSMs vary depending on the number of PM layers, PM shape, number of bridges, and bridge thickness. Additionally, ferrite PMs have a lower coercive force than neodymium (Nd) PMs; therefore, irreversible demagnetization (ID) must be considered, and it is affected by the number of PM layers and PM shape of ML-IPMSMs. Thus, when designing a multilayer IPMSM using ferrite PMs for electric vehicle (EV) traction, all characteristics should be considered. Compared to conventional electrical steel (CES), high-strength electrical steel (HSES) offers advantages in mechanical properties, allowing for greater flexibility in ML shape. Consequently, it is possible to design a shape with improved electrical performance when compared to CES by adjusting the ML shape. In this article, all characteristics of each ML-IPMSM using HSES and CES are reviewed via finite element analysis (FEA), and the benefits of HSES applied motors for high-speed driving motors are presented. To verify the validity of the review content in this article, experiments are conducted on the manufactured motor, and FEA results are compared with the test results.

Ultra-thin 2D Fe3GaTe2 rare-earth free permanent magnet at finite temperatures

Despite extensive studies on permanent magnets (PMs) in bulk-type materials, the possibility of PMs in two-dimensional (2D) materials is barely explored so far. In this work, we systematically investigate temperature dependent magnetic properties of 2D trilayer and four-layer Fe3GaTe2 systems based on the first principle calculations. The calculated Curie temperature (T C) in both trilayer and four-layer structures are 340 K–352 K. Both systems have perpendicular magnetic anisotropy, and the uniaxial anisotropy constant is monotonically decreased with increasing temperature. At 300 K, the 2D Fe3GaTe2 has a coercive field of 0.34 T in the trilayer and it becomes 0.44 T in the four-layer. Besides, both systems have a magnetic hardness parameter κ larger than 1 even at 300 K. We also obtain a maximum energy product (BH)max of 24 kJ m−3 in the trilayer, and it is further increased to 26 kJ m−3 in the four-layer at 300 K. Nonetheless, these (BH)max are decreased by more than two times with including the demagnetization factor. Overall, we obtain that 2D Fe3GaTe2 at 2–3 nm (trilayer and four-layer) thickness possesses the same scale of coercive field and maximum energy product of well-known bulk ferrite PM. Our findings may indicate that the atomically thin 2D system can be a potential rare-earth-free PM for small-scale device applications.

Design and Simulation study of 40 MW PM Generator for the CRAFT

Design studies of two counter rotating permanent magnet (PM) synchronous generators have been performed. The two 40 MW generators have been designed and compared for the Counter Rotating Axis Floating Turbine (CRAFT) with different air-gap diameters. The generators are modelled with validated full physics finite element method (FEM) which also includes dynamic simulations. The simulations are performed by using an electromagnetic model. The model is described by combined field and circuit equations and is solved in a finite element environment. The stator winding of the generators consists of circular cables and the rotor consists of buried ferrite PM. The generator with smaller air-gap diameter will have lower material costs due to smaller frame but higher due to use of more active materials. A comparison of the counter rotating generators with a traditional direct drive has also been performed by maintaining the same voltage but reducing the rotational speed by half. This shows that a generator with a higher rotational speed will have lower material costs due to smaller dimensions and lower weight. Furthermore, a design variation, to reduce the cogging and harmonic content of the voltage by changing the pole shoe, was analyzed. In conclusions, a 40 MW generator design for the CRAFT has successfully been simulated with a multi-physics-FEM. The advantages of using a counter-rotating generator has been established.

Material Tradeoff of Rotor Architecture for Lightweight Low-Loss Cost-Effective Sustainable Electric Drivetrains

The art of the successful design of high-speed electrical machines comes with many challenges in the mass, size, reliability, and energy efficiency. Material engineering of electrical machines has been identified as a key solution for higher power dense electric drivetrains. One of the main challenges at high speed is the eddy-current losses in the active electromagnetic parts, especially magnetic materials and permanent magnets (PMs). This study is devoted to the selection of PM rotor materials using multidisciplinary design optimization for a high-speed electric drivetrain. Beside AC loss minimization, more disciplines are considered, such as the minimization of weight, and cost. Different laminations are investigated with different magnetic properties as well as cost. Additionally, different PMs are optimized considering low-cost ferrite and high-coercivity permanent magnets (HCPMs). Moreover, the optimal materials are identified which have the best balance between loss, weight, cost, ripples. Finally, different rotor designs are prototyped, assembled, and tested using the same stator configuration. Also, the best rotor design is selected, and the electromagnetic performance is measured and compared with conventional designs. The optimal design results in 8% extra torque with at least 20% weight reduction.

Electromagnetic-Thermal Analysis of a Hybrid-Excited Flux Switching Permanent Magnet Generator for Wind Turbine Application

An accurate thermal analysis needs to be performed on the machines with new structures to ensure that their electromagnetic performance is not negatively affected. In this regard, this paper details an investigation into the electromagnetic-thermal analysis of an outer rotor hybrid-excited flux switching permanent magnet generator that gains from ferrite PMs in stator yoke and neodymium PMs in rotor segments. Incorporating ferrite PMs and barriers in the stator core enhances the power density of the proposed generator compared to the basic topology. Also, the temperature of the stator and windings of the HEFSG decreases due to the presence of barriers. As a result, the HEFSG can be a potential candidate for DDWT applications. In this study, the thermal modeling started with a 3-D FEM electromagnetic analysis to calculate the losses as heat sources. Afterward, an accurate thermal network was plotted to elucidate the thermal behaviors between various parts of the generator, where the heat sources, heat transfer coefficients, thermal resistances, and heat capacitances form the thermal characteristics of the network, which was then followed by the 3-D FEM thermal analysis. Finally, the experimental test results from the prototyped generator confirmed the accuracy of the simulation results.