This paper presents new analytic formulas for determining the mutual inductance and the axial mag... more This paper presents new analytic formulas for determining the mutual inductance and the axial magnetic force between two coaxial coils in air, namely a thick circular coil with rectangular cross-section and a thin wall solenoid. The mutual inductance and the magnetic force are expressed as complete elliptical integrals of the first and second kind, Heuman’s Lambda function and one well-behaved
This paper describes the mechanical properties of ferrofluid seals in ironless electrodynamic lou... more This paper describes the mechanical properties of ferrofluid seals in ironless electrodynamic loudspeakers. The motor is constituted of several outer stacked ring permanent magnets. The inner moving part is a piston. In addition, two ferrofluid seals are used which replace the classical suspension. Indeed, these seals fulfill several functions. First, they ensure the airtightness between the loudspeaker faces. Second, they act as bearings and center the moving part. Finally, the ferrofluid seals also exert a pull back force on the moving piston. Both radial and axial forces exerted on the piston are calculated thanks to analytical formulations. Furthermore, the shape of the seal is discussed as well as the optimal quantity of ferrofluid. The seal capacity is also calculated.
The main purpose of the paper is to contribute at presenting a formalism which would be relevant ... more The main purpose of the paper is to contribute at presenting a formalism which would be relevant for interpreting qualitatively the nonlinear harmonic distortion, and more particularly the strong intermodulation, which occur in air in the frequency range (20 Hz-20 kHz) when the vawe is propagating.
This paper presents a comparison of cylindrical and plane air gap magnetic couplings in which the... more This paper presents a comparison of cylindrical and plane air gap magnetic couplings in which the tile permanent magnet polarizations can be either radial or tangential or axial.
This paper presents an analytical method based on the coulombian model of a magnet for studying a... more This paper presents an analytical method based on the coulombian model of a magnet for studying a ferrofluid seal in ironless electrodynamic loudspeakers. Such an approach differs from the ones generally used for studying such geometries because the ferrofluid used is submitted to a very high magnetic field. Consequently, its shape and its mechanical properties depend mainly on the magnetic field produced by the permanent magnets that constitute the ironless structure. The motor is constituted of outer stacked ring permanent magnets and the inner moving part is a piston. In addition, one ferrofluid seal is used for centering the moving part and ensuring the airtightness between the loudspeaker faces. The ferrofluid seal also exerts a pull back force on the moving piston. It is noted that this force depends on the lateral shape of the moving piston. Therefore, the piston profile is analytically studied in this paper. A peculiar attention is given to profiles that ensure the axial pull back force to be proportional to the piston displacement. Furthermore, a geometrical method is presented to design the shape of the ferrofluid seal according to the chosen piston profile. It can be noted that such a profile is elliptical in this study. Then, the magnetic energy of the ferrofluid seal is determined with the analytical expression of the magnetic energy density. Such an expression allows us to calculate the axial force created by the ferrofluid seal for a given profile.
This paper presents a general method for studying the mechanical properties of a ferrofluid seal ... more This paper presents a general method for studying the mechanical properties of a ferrofluid seal by using a three-dimensional analytical approach based on the coulombian model of a magnet. The fundamental Maxwell's equations lead us to define the concept of magnetic energy of the ferrofluid seal by using only the three-dimensional equations of the magnetic field created by ring permanent magnets radially magnetized.
In this paper, we present new expressions for calculating the magnetic field produced by either t... more In this paper, we present new expressions for calculating the magnetic field produced by either tile permanent magnets tangentially magnetized or by radial currents in massive disks. These expressions are fully analytical, that is, we do not use any special functions for calculating them. In addition, they are three-dimensional and can be used for calculating the magnetic field for all regular points in space. The expressions commonly used for calculating the magnetic field produced by radial currents in massive disks are often based on elliptic integrals or semi-analytical forms. We propose in this paper an alternative analytical method that can also be used for tile permanent magnets. Indeed, by using the analogy between the coulombian model and the amperian current model, radial currents in massive disks can be represented by using the fictitious magnetic pole densities that are located on two faces of a tile permanent magnet tangentially magnetized. The two representations are equivalent and thus, the shape of magnetic field produced is the same for all points in space, with a smaller value in the case of it is produced by radial currents in massive disks. Such expressions can be used for realizing easily parametric studies.
This paper presents a general analytical formulation for calculating the three-dimensional magnet... more This paper presents a general analytical formulation for calculating the three-dimensional magnetic field distribution produced by Halbach structures with radial or axial polarization directions. Our model allows us to study tile permanent magnets of various magnetization directions and dimensions. The three magnetic field components are expressed in terms of analytical and semi-analytical parts using only one numerical integration.
This paper presents a thorough study of the magnetic field created by tile permanent magnets unif... more This paper presents a thorough study of the magnetic field created by tile permanent magnets uniformly magnetized in air. To do so, we use the coulombian model for determining the analytical expressions of the three magnetic field components created by the tile magnets. Moreover, various magnetization directions are considered. Indeed, the direction of the magnetization can be radial, tangential or intermediate between radial and tangential. Thus, this analytical study encompasses most of the magnetization possibilities generally encountered in electrical engineering applications.
This paper presents the calculation of the magnetic field created by axially magnetized cylindric... more This paper presents the calculation of the magnetic field created by axially magnetized cylindrical permanent magnets and thin wall solenoids in air. It emphasizes the equivalence of the source models: charged planes and current sheet. It shows that although the starting formulations, magnetic scalar potential, Coulomb's law, vector potential, Biot-Savart's law often depend in the literature on the source nature, they shouldn't. Indeed, it presents the magnetic field calculation for each point of view and explains which lead to analytical solutions. Then it presents the calculation of forces between permanent magnets and shows that it is equivalent to the calculation of the mutual inductance between two coils. 2
The aim of this paper is to determine experimentally the behavior of the ferrofluid seals used in... more The aim of this paper is to determine experimentally the behavior of the ferrofluid seals used in loudspeaker having no viscoelastic suspensions [1]. In this case, the ferrofluid is saturated by a strong magnetic field (300-500 kA/m) relatively to its magnetization (9-32 kA/m). Two ...
The electrodynamic loudspeaker is a strongly nonlinear system. The main causes of nonlinearity ar... more The electrodynamic loudspeaker is a strongly nonlinear system. The main causes of nonlinearity are the nonlinear stiffness of the suspensions and the nonuniform distribution of the magnetic flux density along the air gap in the magnetic circuit. A third cause, the nonlinear voice-coil inductance is often underestimated. The electrical impedance of the voice-coil in the low frequency range is considered usually as a pure resistance, and the influence of its inductance is neglected : this is a reason of the underestimation of its nonlinearity. The voicecoil inductance depends on both the displacement of the voice-coil and the current intensity flowing through it. Additionally, the reluctance force proportional to the square of the current appears in the mechanical part of the system and depends on the voice-coil displacement too. This paper studies the influence of the voice-coil nonlinearity. The differential equation system has been derived and is solved using numerical methods. The harmonic distortions as well as the intermodulation ones have been computed. The results show that the influence of the voice-coil nonlinearity is significant -particularly for intermodulation distortions. This influence is weaker than the influence of the force factor nonlinearity, but stronger than the influence of the suspensions nonlinearity. The influence of the different terms in the nonlinear differential equation system is also tested.
This paper presents an improvement of the calculation of the magnetic field components created by... more This paper presents an improvement of the calculation of the magnetic field components created by ring permanent magnets. The three-dimensional approach taken is based on the Coulombian Model. Moreover, the magnetic field components are calculated without using the vector potential or the scalar potential. It is noted that all the expressions given in this paper take into account the magnetic pole volume density for ring permanent magnets radially magnetized. We show that this volume density must be taken into account for calculating precisely the magnetic field components in the near-field or the far-field. Then, this paper presents the component switch theorem that can be used between infinite parallelepiped magnets whose cross-section is a square. This theorem implies that the magnetic field components created by an infinite parallelepiped magnet can be deducted from the ones created by the same parallelepiped magnet with a perpendicular magnetization. Then, we discuss the validity of this theorem for axisymmetric problems (ring permanent magnets). Indeed, axisymmetric problems dealing with ring permanent magnets are often treated with a 2D approach. The results presented in this paper clearly show that the two-dimensional studies dealing with the optimization of ring permanent magnet dimensions cannot be treated with the same precisions as 3D studies.
This paper presents the exact 3D calculation of the magnetic field produced by a tile permanent m... more This paper presents the exact 3D calculation of the magnetic field produced by a tile permanent magnet whose polarization is both tangential and uniform. Such a calculation is useful for optimizing magnetic couplings or for calculating the magnetic field produced by alternate magnet structures. For example, our 3D expressions can be used for calculating the magnetic field produced by a Halbach structure. All our expressions are determined by using the coulombian model. This exact analytical approach has always proved its accuracy and its usefulness. As a consequence, the tile permanent magnet considered is represented by using the fictitious magnetic pole densities that are located on the faces of the magnet. In addition, no simplifying assumptions are taken into account for calculating the three magnetic field components. Moreover, it is emphasized that the magnetic field expressions are fully three-dimensional. Consequently, the expressions obtained are valid inside and outside of the tile permanent magnet, whatever its dimensions. Such an approach allows us to realize easily parametric studies.
This paper presents the exact analytical formulation of the three components of the magnetic fiel... more This paper presents the exact analytical formulation of the three components of the magnetic field created by a radially magnetized tile permanent magnet. These expressions take both the magnetic pole surface densities and the magnetic pole volume density into account. So, this means that the tile magnet curvature is completely taken into account. Moreover, the magnetic field can be calculated exactly in any point of the space, should it be outside the tile magnet or inside it. Consequently, we have obtained an accurate 3D magnetic field as no simplifying assumptions have been used for calculating these three magnetic components. Thus, this result is really interesting. Furthermore, the azimuthal component of the field can be determined without any special functions. In consequence, its computational cost is very low which is useful for optimization purposes. Besides, all the other expressions obtained are based on elliptic functions or special functions whose numerical calculation is fast and robust and this allows us to realize parametric studies easily. Eventually, we show the interest of this formulation by applying it to one example: the calculation and the optimization of alternate magnetization magnet devices. Such devices are commonly used in various application fields: sensors, motors, couplings, etc. The point is that the total field is calculated by using the superposition theorem and summing the contribution to the field of each tile magnet in any point of the space. This approach is a good alternative to a finite element method because the calculation of the magnetic field is done without any simplifying assumption.
This paper presents new analytic formulas for determining the mutual inductance and the axial mag... more This paper presents new analytic formulas for determining the mutual inductance and the axial magnetic force between two coaxial coils in air, namely a thick circular coil with rectangular cross-section and a thin wall solenoid. The mutual inductance and the magnetic force are expressed as complete elliptical integrals of the first and second kind, Heuman’s Lambda function and one well-behaved
This paper describes the mechanical properties of ferrofluid seals in ironless electrodynamic lou... more This paper describes the mechanical properties of ferrofluid seals in ironless electrodynamic loudspeakers. The motor is constituted of several outer stacked ring permanent magnets. The inner moving part is a piston. In addition, two ferrofluid seals are used which replace the classical suspension. Indeed, these seals fulfill several functions. First, they ensure the airtightness between the loudspeaker faces. Second, they act as bearings and center the moving part. Finally, the ferrofluid seals also exert a pull back force on the moving piston. Both radial and axial forces exerted on the piston are calculated thanks to analytical formulations. Furthermore, the shape of the seal is discussed as well as the optimal quantity of ferrofluid. The seal capacity is also calculated.
The main purpose of the paper is to contribute at presenting a formalism which would be relevant ... more The main purpose of the paper is to contribute at presenting a formalism which would be relevant for interpreting qualitatively the nonlinear harmonic distortion, and more particularly the strong intermodulation, which occur in air in the frequency range (20 Hz-20 kHz) when the vawe is propagating.
This paper presents a comparison of cylindrical and plane air gap magnetic couplings in which the... more This paper presents a comparison of cylindrical and plane air gap magnetic couplings in which the tile permanent magnet polarizations can be either radial or tangential or axial.
This paper presents an analytical method based on the coulombian model of a magnet for studying a... more This paper presents an analytical method based on the coulombian model of a magnet for studying a ferrofluid seal in ironless electrodynamic loudspeakers. Such an approach differs from the ones generally used for studying such geometries because the ferrofluid used is submitted to a very high magnetic field. Consequently, its shape and its mechanical properties depend mainly on the magnetic field produced by the permanent magnets that constitute the ironless structure. The motor is constituted of outer stacked ring permanent magnets and the inner moving part is a piston. In addition, one ferrofluid seal is used for centering the moving part and ensuring the airtightness between the loudspeaker faces. The ferrofluid seal also exerts a pull back force on the moving piston. It is noted that this force depends on the lateral shape of the moving piston. Therefore, the piston profile is analytically studied in this paper. A peculiar attention is given to profiles that ensure the axial pull back force to be proportional to the piston displacement. Furthermore, a geometrical method is presented to design the shape of the ferrofluid seal according to the chosen piston profile. It can be noted that such a profile is elliptical in this study. Then, the magnetic energy of the ferrofluid seal is determined with the analytical expression of the magnetic energy density. Such an expression allows us to calculate the axial force created by the ferrofluid seal for a given profile.
This paper presents a general method for studying the mechanical properties of a ferrofluid seal ... more This paper presents a general method for studying the mechanical properties of a ferrofluid seal by using a three-dimensional analytical approach based on the coulombian model of a magnet. The fundamental Maxwell's equations lead us to define the concept of magnetic energy of the ferrofluid seal by using only the three-dimensional equations of the magnetic field created by ring permanent magnets radially magnetized.
In this paper, we present new expressions for calculating the magnetic field produced by either t... more In this paper, we present new expressions for calculating the magnetic field produced by either tile permanent magnets tangentially magnetized or by radial currents in massive disks. These expressions are fully analytical, that is, we do not use any special functions for calculating them. In addition, they are three-dimensional and can be used for calculating the magnetic field for all regular points in space. The expressions commonly used for calculating the magnetic field produced by radial currents in massive disks are often based on elliptic integrals or semi-analytical forms. We propose in this paper an alternative analytical method that can also be used for tile permanent magnets. Indeed, by using the analogy between the coulombian model and the amperian current model, radial currents in massive disks can be represented by using the fictitious magnetic pole densities that are located on two faces of a tile permanent magnet tangentially magnetized. The two representations are equivalent and thus, the shape of magnetic field produced is the same for all points in space, with a smaller value in the case of it is produced by radial currents in massive disks. Such expressions can be used for realizing easily parametric studies.
This paper presents a general analytical formulation for calculating the three-dimensional magnet... more This paper presents a general analytical formulation for calculating the three-dimensional magnetic field distribution produced by Halbach structures with radial or axial polarization directions. Our model allows us to study tile permanent magnets of various magnetization directions and dimensions. The three magnetic field components are expressed in terms of analytical and semi-analytical parts using only one numerical integration.
This paper presents a thorough study of the magnetic field created by tile permanent magnets unif... more This paper presents a thorough study of the magnetic field created by tile permanent magnets uniformly magnetized in air. To do so, we use the coulombian model for determining the analytical expressions of the three magnetic field components created by the tile magnets. Moreover, various magnetization directions are considered. Indeed, the direction of the magnetization can be radial, tangential or intermediate between radial and tangential. Thus, this analytical study encompasses most of the magnetization possibilities generally encountered in electrical engineering applications.
This paper presents the calculation of the magnetic field created by axially magnetized cylindric... more This paper presents the calculation of the magnetic field created by axially magnetized cylindrical permanent magnets and thin wall solenoids in air. It emphasizes the equivalence of the source models: charged planes and current sheet. It shows that although the starting formulations, magnetic scalar potential, Coulomb's law, vector potential, Biot-Savart's law often depend in the literature on the source nature, they shouldn't. Indeed, it presents the magnetic field calculation for each point of view and explains which lead to analytical solutions. Then it presents the calculation of forces between permanent magnets and shows that it is equivalent to the calculation of the mutual inductance between two coils. 2
The aim of this paper is to determine experimentally the behavior of the ferrofluid seals used in... more The aim of this paper is to determine experimentally the behavior of the ferrofluid seals used in loudspeaker having no viscoelastic suspensions [1]. In this case, the ferrofluid is saturated by a strong magnetic field (300-500 kA/m) relatively to its magnetization (9-32 kA/m). Two ...
The electrodynamic loudspeaker is a strongly nonlinear system. The main causes of nonlinearity ar... more The electrodynamic loudspeaker is a strongly nonlinear system. The main causes of nonlinearity are the nonlinear stiffness of the suspensions and the nonuniform distribution of the magnetic flux density along the air gap in the magnetic circuit. A third cause, the nonlinear voice-coil inductance is often underestimated. The electrical impedance of the voice-coil in the low frequency range is considered usually as a pure resistance, and the influence of its inductance is neglected : this is a reason of the underestimation of its nonlinearity. The voicecoil inductance depends on both the displacement of the voice-coil and the current intensity flowing through it. Additionally, the reluctance force proportional to the square of the current appears in the mechanical part of the system and depends on the voice-coil displacement too. This paper studies the influence of the voice-coil nonlinearity. The differential equation system has been derived and is solved using numerical methods. The harmonic distortions as well as the intermodulation ones have been computed. The results show that the influence of the voice-coil nonlinearity is significant -particularly for intermodulation distortions. This influence is weaker than the influence of the force factor nonlinearity, but stronger than the influence of the suspensions nonlinearity. The influence of the different terms in the nonlinear differential equation system is also tested.
This paper presents an improvement of the calculation of the magnetic field components created by... more This paper presents an improvement of the calculation of the magnetic field components created by ring permanent magnets. The three-dimensional approach taken is based on the Coulombian Model. Moreover, the magnetic field components are calculated without using the vector potential or the scalar potential. It is noted that all the expressions given in this paper take into account the magnetic pole volume density for ring permanent magnets radially magnetized. We show that this volume density must be taken into account for calculating precisely the magnetic field components in the near-field or the far-field. Then, this paper presents the component switch theorem that can be used between infinite parallelepiped magnets whose cross-section is a square. This theorem implies that the magnetic field components created by an infinite parallelepiped magnet can be deducted from the ones created by the same parallelepiped magnet with a perpendicular magnetization. Then, we discuss the validity of this theorem for axisymmetric problems (ring permanent magnets). Indeed, axisymmetric problems dealing with ring permanent magnets are often treated with a 2D approach. The results presented in this paper clearly show that the two-dimensional studies dealing with the optimization of ring permanent magnet dimensions cannot be treated with the same precisions as 3D studies.
This paper presents the exact 3D calculation of the magnetic field produced by a tile permanent m... more This paper presents the exact 3D calculation of the magnetic field produced by a tile permanent magnet whose polarization is both tangential and uniform. Such a calculation is useful for optimizing magnetic couplings or for calculating the magnetic field produced by alternate magnet structures. For example, our 3D expressions can be used for calculating the magnetic field produced by a Halbach structure. All our expressions are determined by using the coulombian model. This exact analytical approach has always proved its accuracy and its usefulness. As a consequence, the tile permanent magnet considered is represented by using the fictitious magnetic pole densities that are located on the faces of the magnet. In addition, no simplifying assumptions are taken into account for calculating the three magnetic field components. Moreover, it is emphasized that the magnetic field expressions are fully three-dimensional. Consequently, the expressions obtained are valid inside and outside of the tile permanent magnet, whatever its dimensions. Such an approach allows us to realize easily parametric studies.
This paper presents the exact analytical formulation of the three components of the magnetic fiel... more This paper presents the exact analytical formulation of the three components of the magnetic field created by a radially magnetized tile permanent magnet. These expressions take both the magnetic pole surface densities and the magnetic pole volume density into account. So, this means that the tile magnet curvature is completely taken into account. Moreover, the magnetic field can be calculated exactly in any point of the space, should it be outside the tile magnet or inside it. Consequently, we have obtained an accurate 3D magnetic field as no simplifying assumptions have been used for calculating these three magnetic components. Thus, this result is really interesting. Furthermore, the azimuthal component of the field can be determined without any special functions. In consequence, its computational cost is very low which is useful for optimization purposes. Besides, all the other expressions obtained are based on elliptic functions or special functions whose numerical calculation is fast and robust and this allows us to realize parametric studies easily. Eventually, we show the interest of this formulation by applying it to one example: the calculation and the optimization of alternate magnetization magnet devices. Such devices are commonly used in various application fields: sensors, motors, couplings, etc. The point is that the total field is calculated by using the superposition theorem and summing the contribution to the field of each tile magnet in any point of the space. This approach is a good alternative to a finite element method because the calculation of the magnetic field is done without any simplifying assumption.
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Papers by Guy Lemarquand