Abstract
The invention relates to a calculation method for designing reluctance systems by balancing the inner and outer system energy using the equation W=.sup.1/2Λ (Θ.sub.a.sup.2+Θ.sub.b.sup.2+2Θ.sub.aΘ.sub.b), where 2Θ.sub.aΘ.sub.b≠0, according to claim 1. The invention further relates to a computer program comprising program code means, in particular a computer program stored on a machine-readable medium, for carrying out the disclosed calculation method when the computer program is executed on a computer.
Claims
1. A calculation method for designing reluctance systems by balancing the inner and outer system energy using the equation W=1/2Λ(Θ.sub.a.sup.2+Θ.sub.b.sup.2+2Θ.sub.aΘ.sub.b), where 2Θ.sub.aΘ.sub.b≠0.
2. The calculation method according to claim 1, wherein a magnetic potential of an electromagnet Θ.sub.b is a value that is dependent on a current (I), which value is to be selected such that W=1/2Λ(Θ.sub.a.sup.2+Θ.sub.b.sup.2+2Θ.sub.aΘ.sub.b)becomes minimal, but is≧1, and the method further comprising: a) using an initial value with I=0 and a second value I.sub.1 ranging between I=0 and I=I.sub.Sättigung (for Θ.sub.b), b) calculating an evaluation value B.sub.1, which is a measure for leveling the balancing between Θ.sub.a and Θ.sub.b with W=1/2Λ(Θ.sub.a.sup.2+Θ.sub.b.sup.2+2Θ.sub.aΘ.sub.b), c) calculating a second evaluation value B.sub.2 for I.sub.2 with the assumption I.sub.1<I.sub.2<<I.sub.Sättigung for Θ.sub.b. d) with B.sub.2<B.sub.1, taking B2 as a new evaluation standard.
3. The calculation method according to claim 1, wherein prior to the energy balancing, the following steps are carried out: a) inputting the data of the reluctance system partners; b) determining the magnetic resistances as a function of the input data; c) outputting the values of the values obtained in step b) as spline functions; d) determining the magnetic intermediate range reluctances; e) establishing at least one non-linear equation system with the values generated in steps b) through d); f) leveling the nonlinearity of the equation system according to step e) by means of a mathematical model
ψ(αn)φ(αn)Rmag(αn) in order to obtain the output values.
4. The calculation method according to claim 3, wherein the leveling of the nonlinearity of the equation system, step f), is carried out by using the derived stress tensor P=−∫.sub.0.sup.H′=HμH′dH+μH.sub.x.sup.2; μH.sub.xH.sub.y; μH.sub.xH.sub.2.
5. The calculation method according to at claim 1, wherein the reluctance system is an electric motor consisting of a rotor and a stator.
6. The calculation method according to claim 3, wherein method step d) according to claim 3 is replaced by determining the air gap resistances as a function of the rotor position α.sub.n and wherein the last step according to claim 3 is followed by repeating the calculation of the air gap reluctances n times with the now obtained values for each rotor position α.sub.n.
7. The calculation method according to claim 6, wherein the last step is followed by another step, in which the induced voltage of the electric motor and the torque thereof are determined.
8. The calculation method according to claim 3, wherein the last step is followed by another step, in which the permanent magnet is dimensioned.
9. The calculation method according to claim 3, wherein an equivalent circuit diagram is used for determining the spline functions, which equivalent circuit diagram consists of a combination of a voltage source equivalent circuit diagram and a current source equivalent circuit diagram.
10. (canceled)
11. A non-transitory computer readable medium comprising software code sections adapted to perform a calculation method for designing reluctance systems by balancing the inner and outer system energy using the equation W=1/2Λ(Θ.sub.a.sup.2+Θ.sub.b.sup.2+2Θ.sub.aΘ.sub.b), where 2Θ.sub.aΘ.sub.b≠0
Description
BRIEF DESCRIPTION OF THE DRAWINGS
[0135] FIGS. 1, 2, 3 show the magnetization functions of the air gap, the soft iron and the permanent magnet.
[0136] FIG. 4 shows the change of the permeability despite the external field being constant.
[0137] FIG. 5 shows a comparison between the electromagnet and the permanent magnet.
[0138] FIG. 6 shows a plot of the mechanical work in relation to the magnetic volume of the permanent magnet and the electromagnet.
[0139] FIG. 7 shows a simple sketch of a permanent magnet having an excitation coil.
[0140] FIG. 8 shows an equivalent circuit diagram with Θ.sub.a and Θ.sub.b, which is considered to belong to the state of science and art and has been used so far.
[0141] FIG. 9 shows a model of an electromagnet.
[0142] FIG. 10 shows the magnetization characteristics of the electromagnet and the permanent magnet as well as the shear straight with the corresponding geometrical relationships.
[0143] FIG. 11 also shows the magnetization characteristics of the electromagnet and the permanent magnet as well as the shear straight and also determined measurement values for different air gap sizes.
[0144] FIG. 12 shows a variant of a flow chart for calculating reluctance system partners.
[0145] FIG. 13 shows another variant of a flow chart for calculating the reluctance system partners.
[0146] FIG. 14 shows a combination of the polygonal chain and the interpolation polynomial.
[0147] FIG. 15 shows a modulation function with six partial polynomials.
[0148] FIGS. 16, 17 show the occurrence of lateral pressure and longitudinal tension in relation to the magnetization function.
[0149] FIGS. 18, 19 compare the linear case with the nonlinear case of a magnetization in a vector diagram.
[0150] FIG. 20 shows a two-dimensional vector diagram for a nonlinear magnetization function of iron.
[0151] FIG. 21 shows a cut of the stator sheet metal of a three-phase motor.
[0152] FIG. 22 shows a partial section of a stator pole and of a rotor arranged on the opposite side.
[0153] FIG. 23 shows a development of the stator/rotor.
[0154] FIG. 24 shows the statically measured torque depicted over different currents as a function of the angle α.
[0155] FIGS. 25, 26 show the current profile over time, which was correlated with the motor steps.
[0156] FIG. 27 shows the conventional illustration of the voltage source equivalent circuit diagram and the current source equivalent circuit diagram.
[0157] FIG. 28 shows the equivalent circuit diagram that takes the influence of the reluctance system partners into consideration.
[0158] FIGS. 29, 30 show the energy density distribution of the electromagnet and the permanent magnet.
[0159] FIGS. 31, 32 show the mechanical work in relation to the magnetic volume of the electromagnet and the permanent magnet.
DETAILED DESCRIPTION OF THE INVENTION
[0160] FIGS. 1, 2, 3 show the magnetization functions of the air gap, the soft iron and the permanent magnet. FIG. 1 shows a linear magnetization function in the air, FIG. 2 shows a nonlinear magnetization function for soft iron and FIG. 3 shows a permanent magnetization function for permanent magnets.
[0161] FIG. 4 shows the change of the permeability despite the external field being constant. When displacements occur in a constant external magnetic field, the permeability μ changes in the fixed point in space in a constant magnetic field H.
[0162] FIG. 5 shows a comparison of the electromagnet and the permanent magnet with the air gap measure l.sub.e/2 and the inner measure l.sub.i/2 with a current I and a winding number N. The same also applies to the permanent magnet.
[0163] FIG. 6 shows a plot of the mechanical work in relation to the magnetic volume of the permanent magnet and the electromagnet, which are herein compared.
[0164] FIG. 7 shows a simple sketch of an electromagnet.
[0165] FIG. 8 shows an equivalent circuit diagram with Θ.sub.a and Θ.sub.b, which is considered to belong to the state of science and art and has been used so far.
[0166] FIG. 9 shows a model of an electromagnet with a yoke 1, a core 2, two armatures 3, 4 and an air gap 5.
[0167] FIG. 10 shows the magnetization characteristics of the electromagnet and the permanent magnet as well as the shear straight with the corresponding geometrical relationships, wherein 1 is the intersection point between the magnetization characteristic of the permanent magnet and the abscissa, 2 is the shear straight of the reluctance system, 3 is the intersection point between the magnetization characteristic of the permanent magnet and the shear straight with I=0, 4 is the point on that shear straight that, with point 5, geometrically corresponds to Θb, 5 is the corresponding point on the ordinate, 6 is the recalculated working point of the reluctance system, at which the energy balance becomes a minimum, 7 is the displaced lower corner point of the parallelogram 4-5 6-7 with a width of Θb and a height of Θa (or vice versa)
[0168] FIG. 11 shows the relationships of a reluctance system obtained by measurement, wherein 1 is the magnetization characteristic of the permanent magnet with a shear straight, 2 for an air gap width of 2 mm, 3 is the magnetization characteristic of the electromagnet, 4 is the shear straight of a reluctance system with an air gap width of 4 mm, 5 is a collection of measurement values on the magnetization function of the permanent magnet with an air gap width of 2 mm, 6 are the measured values of the magnetization function of the electromagnet, 7 is the intersection point of the magnetization function with the ordinate, 8 is the measured external working point of the electromagnet, 9 is the conventionally calculated working point of the permanent magnet and the electromagnet, 10 is the saturation point of the electromagnet, 11 is the measured working point of the permanent magnet and the electromagnet
[0169] FIG. 12 shows a flow chart of a calculation algorithm, which can be used for calculating geometrically complex reluctance systems.
[0170] A new equation system is solved for each position of the electromagnet, as different air gap reluctances must be taken into consideration for each position. It starts with entering the geometries of the positions of the system partners (angle and distance) under consideration of the respective model. This results in a frame file determining the resistances in the iron parts. Depending on the input, these are output as constant values or as spline functions. On the basis of the considered rotor position α.sub.n, the air gap resistances are determined. All resistances and magnetic voltage sources serve as input data for the calculation program. The nonlinear equation system is calculated in a separate calculation file, which is retrieved from the frame file and contains the energetically balanced relevant quantities. Subsequently, the obtained values are evaluated, on the basis of which calculation the calculation of the separate calculation file is either terminated or recalculated with a new initial value. The equation system can be solved in several iteration steps. The zero vector is chosen as initial value. The output values comprise potentials, flux values and resistances of the magnetic circuit. This is repeated for each angle αn. At the end of the calculation, all results are summarized and the voltage induced in the coils and the branches as well as the torque of the system are determined.
[0171] FIG. 13 shows the concretized variant for calculating an electromotor.
[0172] FIG. 14 shows the unsteadiness of a polygonal chain after the first derivation.
[0173] FIG. 15 shows a modulation function with six partial polynomials.
[0174] FIGS. 16, 17 show the occurrence of lateral pressure and longitudinal tension in relation to the magnetization function B as a function of H, wherein the tensional stresses differ from the compressive stresses.
[0175] FIGS. 18, 19 compare the linear case with the nonlinear case of a magnetization in a vector diagram.
[0176] FIG. 20 shows a two-dimensional vector diagram for a nonlinear magnetization function of iron.
[0177] FIG. 21 shows a cut of the stator sheet metal of a three-phase motor.
[0178] FIG. 22 shows a partial section of a stator pole and of a rotor arranged on the opposite side.
[0179] FIG. 23 shows a development of the stator/rotor.
[0180] FIG. 24 shows the statically measured torque depicted over different currents as a function of the angle α.
[0181] FIGS. 25, 26 show the current profile over time, which was correlated with the motor steps.
[0182] FIG. 27 shows the illustration of the voltage source equivalent circuit diagram and the current source equivalent circuit diagram, which take the inner energy densities under reciprocal influence into consideration.
[0183] FIG. 28 shows the equivalent circuit diagram that takes the influence of the reluctance system partners into consideration.
[0184] FIGS. 29, 30 show the energy density distribution of the electromagnet and the permanent magnet.
[0185] FIGS. 31, 32 show the mechanical work in relation to the magnetic volume of the electromagnet and the permanent magnet.
[0186] While the invention has been described with reference to exemplary embodiments and applications scenarios, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted for elements thereof without departing from the scope of the claims. Therefore, it is intended that the invention not be limited to the particular embodiments disclosed, but that the invention will include all embodiments falling within the scope of the appended claims and can be applied to various application in the industrial as well as commercial field.
[0187] The following applies:
SIGNS AND SYMBOLS USED THROUGHOUT THE INVENTION
[0188] Ā vector area [0189] B magnetic flux density vector [0190] D electric flux density vector [0191] Ē electric field strength vector [0192] G region [0193] H magnetic field strength vector [0194] I amperage [0195] J spatial current density vector [0196] K random constant [0197] M magnetization vector [0198] P electrical polarization vector [0199] P.sub.th thermal power dissipation [0200] P(x) Lagrange interpolation polynomial [0201] R reduction factor [0202] Ū general vector [0203] V force function (general) [0204] V.sub.m magnetic force function [0205] V.sub.el electric force function [0206] V vector potential [0207] W energy (general) [0208] W.sub.m magnetic energy [0209] W.sub.el electric energy [0210] W.sub.m mec mechanical energy, caused by the change in the magnetic energy [0211] W.sub.el mec mechanical energy, caused by the change in the electric energy [0212] W.sub.mec mechanical energy [0213] F.sub.q general force component [0214] W.sub.e outer energy [0215] W.sub.i inner energy [0216] H.sub.e external magnetic field strength [0217] H.sub.i internal magnetic field strength [0218] [Ā, B] vector product [0219] (Ā, B) scalar product [0220] grad gradient [0221] Grad area gradient [0222] div divergency [0223] Div area divergency [0224] rot rotation [0225] Rot area rotation [0226] ∇ nabla operator [0227] ∂ partial derivation [0228] ∂ change in the fixed point in space [0229] δ![custom-character]()
infinitely small displacement [0230] ε permittivity [0231] μ permeability [0232] μ.sub.d differential permeability [0233] dτ volume element [0234] ρ.sub.m magnetic spatial density [0235] Λ magnetic permeance [0236] λ coefficient [0237] Σ summation sign [0238] σ potential of a double occupancy [0239] ψ coil flux [0240] α angle [0241] β angle [0242] Θ magnetic potential [0243] Δ delta operator [0244] Δdesignation of a difference [0245] d′ total differential [0246] d change in the fixed substantial point [0247] d total differential [0248] dĀ vectorial area element [0249] dt time element [0250] ds vectorial line element [0251] a.sub.m constant for boundary condition [0252] b.sub.m constant for boundary condition [0253] d.sub.m constant for boundary condition [0254] e index for external [0255] f volume force (specific) [0256] i instantaneous value of the amperage [0257] ī unit vector in x direction [0258] j unit vector in y direction [0259] k unit vector in z direction [0260] l length (general) [0261] l.sub.i internal length [0262] l.sub.e external length [0263] n normal unit vector [0264] p normal unit vector [0265] p specific area force [0266] p.sub.21 specific area force on interfaces [0267] q general coordinate [0268] t parameter [0269] u potential function [0270] u scalar potential [0271] V.sub.el electric force density function [0272] V.sub.m magnetic force density function [0273] W.sub.el electric energy density [0274] W.sub.m magnetic energy density [0275] z general complex number [0276] {right arrow over (p)} fictive stress state in the non-linear medium [0277] ψ(αn) magnetic interlinking flux dependent on the angle α [0278] φ(αn) magnetic flux dependent on the angle α [0279] Rmag(αn) magnetic resistance dependent on the angle α
