CN111859694B - Heat source loss calculation method for permanent magnet magnetic coupler - Google Patents
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Abstract
The invention discloses a method for calculating heat source loss of a permanent magnetic coupler, belongs to the field of permanent magnetic transmission, and relates to a method for calculating heat source loss of a permanent magnetic coupler. The method comprises the steps of firstly obtaining the magnetic resistance of each part according to the geometric dimensions of a conductor copper disc, a conductor copper disc back iron, a permanent magnet disc, a permanent magnet and a permanent magnet disc back iron which form the permanent magnet magnetic coupler, and establishing an equivalent magnetic circuit model of the permanent magnet magnetic coupler. According to kirchhoff's law, the effective magnetic induction intensity passing through the conductor copper plate is obtained by considering the nonuniformity of magnetic field intensity distribution and the diversity of loss forms. And obtaining the heat source loss of the permanent magnetic coupler through the proportion and the correction coefficient of the heat source loss form. The method is simple in calculation, efficient, reliable, high in calculation accuracy and wide in applicability, can achieve the calculation task of heat source loss of the permanent magnet magnetic force adjusting coupler, and provides technical support for design and operation of the permanent magnet magnetic force coupler.
Description
Technical Field
The invention belongs to the field of permanent magnet magnetic transmission, and relates to a method for calculating heat source loss of a permanent magnet magnetic coupler.
Background
Along with the update and rapid promotion of scientific technology, the contradiction between energy and environment is increasingly prominent, and the requirement for a transmission mode is higher and higher. As a new generation of transmission device, compared with the traditional transmission equipment, the permanent magnetic coupler has the obvious advantages of simplicity, reliability, safety, environmental protection, low maintenance cost, stability, high efficiency and the like, and gradually gains attention from the fields of coal, chemical engineering, electric power and other important engineering. The core part of the permanent magnetic force coupler is a conductor copper disc and a permanent magnet disc, the conductor copper disc cuts magnetic lines of force under a magnetic field generated by the permanent magnet disc, and the surface of the conductor copper disc can generate strong eddy current to generate heat, so that the permanent magnetic force coupler part is even caused to fail, and therefore the heat source loss of the permanent magnetic force coupler can realize accurate prediction of a heating position, and further the high efficiency and the high reliability of the operation of the permanent magnetic force coupler are guaranteed. At present, heat source loss calculation of a permanent magnet magnetic coupler is mainly a finite element method, the finite element method is good in calculation accuracy, but the finite element method is complex in procedure, complex in modeling and long in calculation time, grids of different sizes need to be established according to differences of different parts, and the finite element method is poor in flexibility and has great limitation.
Aiming at the calculation of the heat source loss of the permanent magnetic coupler, the Temp field finite element analysis of the permanent magnetic coupler was published in 2017 on the coal mine electromechanical in 5 th by Chenhongqu of the coal science research institute, Pro/E and Ansys Workbench software are adopted to model, solve and analyze the permanent magnetic coupler, so that the heat source loss of the permanent magnetic coupler under different slip conditions is obtained, and a safe working slip value is given. The method has good precision, but the modeling time is long, the finite element analysis steps are complicated, the design guidance of complex parts is greatly limited, and the application range is limited.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, and provides a method for calculating the heat source loss of a permanent magnet magnetic coupler. And obtaining the effective magnetic induction intensity of the conductor copper plate and the system heat source loss through the proportion and the correction coefficient of the heat source loss form. The method has the advantages of simple calculation, high efficiency, reliability, high calculation precision and wide applicability, and provides technical support for the design and operation of the permanent magnetic coupler.
The technical scheme adopted by the invention is a heat source loss calculation method of a permanent magnetic coupler, which is characterized by comprising the following steps of firstly obtaining the magnetic resistance of each part according to the geometric dimension of each part forming the permanent magnetic coupler, and obtaining an equivalent magnetic circuit model of the permanent magnetic coupler by considering the electromagnetic field characteristic of the permanent magnetic coupler; obtaining the effective magnetic induction intensity passing through the conductor copper plate according to kirchhoff's law; considering the nonuniformity of magnetic field intensity distribution and the diversity of loss forms, correcting a calculation formula by adopting a correction coefficient to obtain the heat source loss of the permanent magnetic coupler; the calculation method comprises the following specific steps:
firstly, establishing an equivalent magnetic circuit model of each part of the permanent magnetic coupler
The parts of the permanent magnetic coupler are composed of a conductor copper disc back iron 1, a conductor copper disc 2, a permanent magnet disc 3, a permanent magnet 4 and a permanent magnet disc back iron 5, and the magnetic resistance corresponding to each part can be calculated according to the geometrical structure of the parts. First according to the width w of the permanent magnet 4 pm Thickness l of permanent magnet 4 pm Center-adjacent distance tau of permanent magnets 4 p The adjacent spacing tau of the permanent magnets 4 m Vacuum magnetic permeability mu 0 And the relative magnetic permeability mu of the permanent magnet 4 pm Calculating the main magnetic resistance R of the permanent magnet pm Comprises the following steps:
by the width w of the permanent magnet 4 pm Thickness l of copper plate 2 of conductor cs Thickness of adjacent air gap l a Center-adjacent distance tau of permanent magnets 4 p The adjacent spacing tau of the permanent magnets 4 m Vacuum magnetic permeability mu 0 The relative permeability mu of the copper plate 2 of the conductor cs And relative gas permeability mu a Calculating the main magnetic resistance R of the copper disk of the conductor cs Comprises the following steps:
by the width w of the permanent magnet 4 pm Thickness l of conductor copper disc back iron 1 b1 Permanent magnet disc back iron 5Thickness l of b5 Center-adjacent distance tau of permanent magnets 4 p The adjacent spacing tau of the permanent magnets 4 m Vacuum magnetic permeability mu 0 And relative permeability mu of back iron b Calculating the main reluctance R of the back iron b Is composed of
By the coercive force H of the permanent magnet 4 pm And thickness l of permanent magnet 4 pm Can calculate the magnetomotive force F of the permanent magnet pm Comprises the following steps:
F pm ＝H pm l pm (4)
according to the width w of the permanent magnet 4 pm Thickness l of copper plate 2 of conductor cs Thickness of adjacent air gap l a The adjacent distance tau between the permanent magnets 4 m Vacuum magnetic permeability mu 0 And relative gas permeability mu a The air gap leakage reluctance Rl can be calculated a Comprises the following steps:
according to the width w of the permanent magnet 4 pm Thickness l of permanent magnet 4 pm The adjacent spacing tau of the permanent magnets 4 m Vacuum magnetic permeability mu 0 And relative gas permeability mu a The leakage magnetic resistance Rl of the permanent magnet can be calculated pm Comprises the following steps:
and connecting the magnetic resistances of the parts by using wires by combining the electromagnetic field property and the direction of the magnetic force line, so as to establish an equivalent magnetic circuit model of the permanent magnetic coupler.
Second, calculating the effective magnetic induction intensity passing through the conductor copper plate
And (3) combining the equivalent magnetic circuit model obtained in the first step with kirchhoff's law, namely the magnetic potentials of the loops are equal, and obtaining a basic magnetic resistance equation as follows:
in the formula (7), phi e For effective magnetic flux through the copper plates of the conductors, phi l To leak magnetic flux, phi 0 Is the main flux.
By means of the formula (7), the effective magnetic flux phi passing through the copper plate of the conductor can be simplified e Comprises the following steps:
obtaining the effective magnetic induction B passing through the conductor copper plate according to the basic relation of the magnetic flux and the magnetic induction e Comprises the following steps:
B e ＝2φ e /[w pm (τ p -τ m )] (9)
thirdly, calculating the heat source loss of the permanent magnetic coupler
In the operation process of the permanent magnet magnetic coupler, eddy current rings, namely loss sources, are generated in the conductor copper disc area corresponding to each permanent magnet. Heat source loss Q per swirl ring 1 Is composed of
k＝μ 0 σ cs Δωr av l cs /[2(l a +l cs )] (11)
In the formula (10), r 1 Is the inner diameter of the conductor copper disc 2, r 2 Is the outer diameter of the conductor copper disc 2, r av Is the average radius, σ, of the permanent magnet 4 cs For the electrical conductivity of the conductor copper disc 2, Δ ω is the angular velocity of the conductor copper disc 2 relative to the permanent magnet disc 3, k is a reference coefficient and is given by equation (11).
System losses from mechanical losses and eddy current ring lossesThe loss composition is characterized in that the eddy current ring loss accounts for 95%, the mechanical loss accounts for only 5%, p permanent magnets and the nonuniformity of magnetic field distribution in the permanent magnet magnetic coupler are considered, and the correction coefficient k is increased according to the formula (10) c Therefore, the heat source loss Q of the permanent magnetic coupler is:
in the formula (12), tanh is a mathematical expression symbol of an inverse trigonometric function.
Finally, the heat source loss of the permanent magnet magnetic coupler is obtained by the formula (12).
The method has the advantages that the real geometric structure size and the actual magnetic path trend of the permanent magnetic force coupler are considered, the relation between the magnetic resistances of all parts is analyzed, an equivalent magnetic path model of the permanent magnetic force coupler is obtained, and the effective magnetic induction intensity penetrating through the conductor copper plate is obtained according to the kirchhoff law. Meanwhile, in consideration of the loss proportion and the nonuniformity of magnetic field distribution, a clear and simple analytical model is provided by adopting a correction coefficient correction formula, and finally the heat source loss of the permanent magnet magnetic coupler is calculated. The method for calculating the heat source loss of the permanent magnet magnetic coupler can complete the task of accurately calculating the heat source loss of the permanent magnet magnetic coupler, has the advantages of simple and convenient steps, good precision and short time consumption, and has good guiding significance for the design and operation monitoring of the permanent magnet magnetic coupler in practical engineering application.
Drawings
Fig. 1 is a flow chart of a method for calculating heat source loss of a permanent magnet magnetic coupler according to the present invention.
FIG. 2 is a schematic diagram of a permanent magnet magnetic coupler geometry, wherein 1-conductor copper disk back iron, 2-conductor copper disk, 3-permanent magnet disk, 4-permanent magnet, 5-permanent magnet disk back iron
FIG. 3 is an equivalent magnetic circuit model of a permanent magnet magnetic coupler, wherein R b Conductor copper disc back iron main reluctance, R cs Conductor copper disc main reluctance, Rl a Air gap leakage reluctance, Rl pm Permanent magnet leakage reluctance, R pm Permanent magnet main reluctance, F pm -permanent magnet magnetomotive force.
Detailed Description
The invention will be further explained and implemented with reference to the drawings and technical solutions.
In the embodiment, a heat source of a permanent magnetic coupler with the rated rotating speed of 1500r/min is selected for calculation.
Wherein, the rated rotation speed is 1500r/min, the inner diameter r of the conductor copper plate 2 of the permanent magnetic force coupler 1 87.5mm, the outer diameter r of the conductor copper disc 2 2 187.5mm, average radius r of permanent magnet 4 av 150mm, the electrical conductivity σ of the conductor copper disc 2 cs 58000000S/m, the angular velocity delta omega of the conductor copper disc relative to the permanent magnet disc is 2rad/S, the width w of the permanent magnet 4 pm 50mm, thickness l of the permanent magnet 4 pm 25mm, thickness l of conductor copper disc back iron 1 b1 10mm, thickness l of permanent magnet disc back iron 5 b5 10mm, thickness l of the conductor copper plate 2 cs 10mm, thickness l of adjacent air gap a 5mm, the adjacent distance tau between the centers of the permanent magnets 4 p 78.5mm, the permanent magnets 4 being adjacent to each other by a distance tau m 28.5mm, vacuum permeability μ 0 Is 4 pi x 10 -7 H/m, relative permeability μ of permanent magnet 4 pm 1.05, relative permeability μ of the conductive copper disc 2 cs Is 0.99, and a gas relative permeability mu a 1, relative permeability of back iron μ b To 2000, the coercive force H of the permanent magnet 4 pm Is 900 KA/m.
The invention provides a flow chart of a heat source loss calculation method of a permanent magnet magnetic coupler, which is shown in figure 1.
The specific steps of the calculation method are as follows;
firstly, establishing an equivalent magnetic circuit model of each part of the permanent magnetic coupler
The permanent magnet magnetic coupler consists of a conductor copper disc back iron 1, a conductor copper disc 2, a permanent magnet disc 3, a permanent magnet 4 and a permanent magnet disc back iron 5, as shown in figure 2. Based on the geometry of each component part, the magnetic reluctance corresponding to each component part can be calculated. First according to the width w of the permanent magnet 4 pm Thickness l of permanent magnet 4 pm Permanent magnet 4 central phaseAdjacent spacing τ p The adjacent spacing tau of the permanent magnets 4 m Vacuum magnetic permeability mu 0 And the relative permeability mu of the permanent magnet 4 pm Calculating the main reluctance R of the permanent magnet according to the formula (1) pm Is 1.52 multiplied by 10 7 H -1 。
By the width w of the permanent magnet 4 pm Thickness l of copper plate 2 of conductor cs Thickness of adjacent air gap l a Center-to-center spacing τ of permanent magnets 4 p The adjacent spacing tau of the permanent magnets 4 m Vacuum magnetic permeability mu 0 The relative permeability mu of the copper plate 2 of the conductor cs And relative gas permeability mu a Calculating the main magnetic resistance R of the copper plate of the conductor according to the formula (2) cs Is 1.01X 10 7 H -1 。
By the width w of the permanent magnet 4 pm Thickness l of conductor copper disc back iron 1 b1 Thickness l of permanent magnet disc back iron 5 b5 Center-adjacent distance tau of permanent magnets 4 p The adjacent spacing tau of the permanent magnets 4 m Vacuum magnetic permeability mu 0 And relative permeability mu of back iron b Calculating the back iron main magnetic resistance R according to the formula (3) b Is 2.9 multiplied by 10 6 H -1 。
By the coercive force H of the permanent magnet 4 pm And the thickness l of the permanent magnet 4 pm Can calculate the magnetomotive force F of the permanent magnet pm 22500A.
According to the width w of the permanent magnet 4 pm Thickness l of copper plate 2 of conductor cs Thickness of adjacent air gap l a The adjacent spacing tau of the permanent magnets 4 m Vacuum magnetic permeability mu 0 And relative gas permeability mu a From equation (5), the air gap leakage reluctance Rl can be calculated a Is 4.92 multiplied by 10 7 H -1 。
According to the width w of the permanent magnet 4 pm Thickness l of permanent magnet 4 pm The adjacent distance tau between the permanent magnets 4 m Vacuum magnetic permeability mu 0 And relative gas permeability mu a From equation (6), the leakage reluctance Rl of the permanent magnet can be calculated pm Is 6.56X 10 7 H -1 。
Combining the electromagnetic field property and the direction of the magnetic force line, the magnetic resistances of the parts are connected by the conducting wire, and an equivalent magnetic circuit model of the permanent magnetic coupler is established, as shown in fig. 3.
Second, calculating the effective magnetic induction intensity passing through the conductor copper plate
Obtaining an equivalent magnetic circuit model obtained in the first step by combining kirchhoff's law, namely the magnetic potentials of the loops are equal to obtain a basic magnetic resistance equation (7) and equations (8) - (9), and obtaining the effective magnetic induction B passing through the conductor copper plate according to the basic relation between the magnetic flux and the magnetic induction e And was 0.55T.
Thirdly, calculating the heat source loss of the permanent magnetic coupler
In the operation process of the permanent magnet magnetic coupler, eddy current rings, namely heat sources, are generated in the conductor copper disc area corresponding to each permanent magnet. Calculating the heat source loss Q of each vortex ring according to the formulas (10) to (11) 1 Is 1003W.
The system loss consists of mechanical loss and eddy current loop loss, wherein the eddy current loop loss accounts for 95%, the mechanical loss only accounts for 5%, 12 permanent magnets and the nonuniformity of magnetic field distribution in the permanent magnet magnetic coupler are considered, and a correction coefficient k is increased according to the formula (10) c Therefore, the heat source loss Q of the permanent magnet magnetic coupler is calculated to be 434W by equation (12).
The invention fully considers the nonuniformity and the loss proportion of the magnetic field distribution of the permanent magnetic coupler, corrects the formula by adopting the correction coefficient, provides a clear and simple analytic model, and finally calculates the heat source loss of the permanent magnetic coupler. The method for calculating the heat source loss of the permanent magnet magnetic coupler can complete the task of accurately calculating the heat source loss of the permanent magnet magnetic coupler, has the advantages of simple and convenient steps, good precision and short time consumption, and has good guiding significance for the design and operation monitoring of the permanent magnet magnetic coupler in practical engineering application.
Claims (1)
1. A method for calculating heat source loss of a permanent magnetic coupler is characterized by comprising the steps of firstly, obtaining the magnetic resistance of each part according to the geometric dimension of each part forming the permanent magnetic coupler, and obtaining an equivalent magnetic circuit model of the permanent magnetic coupler by considering the electromagnetic field characteristic of the permanent magnetic coupler; obtaining the effective magnetic induction intensity passing through the conductor copper plate according to kirchhoff's law; considering the nonuniformity of magnetic field intensity distribution and the diversity of loss forms, correcting a calculation formula by adopting a correction coefficient to obtain the heat source loss of the permanent magnetic coupler; the calculation method comprises the following specific steps:
firstly, establishing an equivalent magnetic circuit model of each part of the permanent magnetic coupler
The permanent magnetic coupler consists of a conductor copper disc back iron (1), a conductor copper disc (2), a permanent magnet disc (3), a permanent magnet (4) and a permanent magnet disc back iron (5), and the magnetic resistance corresponding to each component is calculated according to the geometric structure size of each component;
firstly according to the width w of the permanent magnet (4) pm Thickness l of permanent magnet (4) pm Center adjacent distance tau of permanent magnet (4) p The adjacent distance tau between the permanent magnets (4) m Vacuum magnetic permeability mu 0 And the relative permeability mu of the permanent magnet (4) pm Calculating the main magnetic resistance R of the permanent magnet (4) pm Comprises the following steps:
from the width w of the permanent magnet (4) pm Thickness l of copper plate (2) of conductor cs Thickness of adjacent air gap l a Center adjacent distance tau of permanent magnet (4) p The adjacent spacing tau of the permanent magnets (4) m Vacuum magnetic permeability mu 0 The relative magnetic permeability mu of the conductor copper disc (2) cs And relative gas permeability mu a Calculating the main magnetic resistance R of the conductor copper disc (2) cs Comprises the following steps:
from the width w of the permanent magnet (4) pm Thickness l of conductor copper disc back iron (1) b1 Thickness l of permanent magnet disc back iron (5) b5 Center adjacent distance of the permanent magnets (4)τ p The adjacent spacing tau of the permanent magnets (4) m Vacuum magnetic permeability mu 0 And yoke relative magnetic permeability mu b Calculating the main magnetic resistance R of the back iron of the copper disc of the conductor b Comprises the following steps:
by the coercive force H of the permanent magnet (4) pm And the thickness l of the permanent magnet (4) pm Calculating the magnetomotive force F of the permanent magnet pm Comprises the following steps:
F pm ＝H pm l pm (4)
according to the width w of the permanent magnet (4) pm Thickness l of the conductor copper plate (2) cs Thickness of adjacent air gap l a The adjacent spacing tau of the permanent magnets (4) m Vacuum magnetic permeability mu 0 And relative gas permeability mu a Calculating the air gap leakage reluctance Rl a Comprises the following steps:
according to the width w of the permanent magnet (4) pm Thickness l of permanent magnet (4) pm The adjacent spacing tau of the permanent magnets (4) m Vacuum magnetic permeability mu 0 And relative gas permeability mu a Calculating leakage magnetic resistance Rl of permanent magnet pm Comprises the following steps:
combining the electromagnetic field property and the direction of magnetic force lines, connecting the magnetic resistance of each part by using a lead, and establishing an equivalent magnetic circuit model of the permanent magnetic coupler;
second, calculating the effective magnetic induction intensity passing through the conductor copper plate
And (3) combining the equivalent magnetic circuit model obtained in the first step with kirchhoff's law, namely the magnetic potentials of the loops are equal, and obtaining a basic magnetic resistance equation as follows:
in the formula (7), phi e For effective magnetic flux through the copper plates of the conductors, phi l To leak magnetic flux, phi 0 Is the main magnetic flux;
the effective magnetic flux phi passing through the copper plate of the conductor is simplified by the formula (7) e Comprises the following steps:
obtaining the effective magnetic induction B passing through the conductor copper plate according to the basic relation of the magnetic flux and the magnetic induction e Comprises the following steps:
B e ＝2φ e /[w pm (τ p -τ m )] (9)
thirdly, calculating the heat source loss of the permanent magnetic coupler
In the operation process of the permanent magnetic coupler, a vortex ring, namely a loss source, is generated in a conductor copper disc area corresponding to each permanent magnet; heat source loss Q per swirl ring 1 Is composed of
k＝μ 0 σ cs Δωr av l cs /[2(l a +l cs )] (11)
In the formula (10), r 1 Is the inner diameter of the copper plate 2 of the conductor, r 2 Is the outer diameter of the conductor copper disc 2, r av Is the average radius, σ, of the permanent magnet 4 cs Is the electrical conductivity of the conductor copper disc 2, Δ ω is the angular velocity of the conductor copper disc 2 relative to the permanent magnet disc 3, k is the reference coefficient;
system losses from mechanical losses and swirl ringsA loss composition in which eddy current ring losses account for 95% and mechanical losses account for only 5%; meanwhile, considering that p permanent magnets and the nonuniformity of magnetic field distribution exist in the permanent magnetic coupler, the correction coefficient k is increased according to the formula (10) c Therefore, the heat source loss Q of the permanent magnetic coupler is:
in the formula (12), tanh is a mathematical expression symbol of an inverse trigonometric function;
finally, the heat source loss Q of the permanent magnet magnetic coupler is obtained from the formula (12).
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