CN110457733B - Rapid calculation method for axial force of permanent magnet coupler - Google Patents
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Abstract
The invention discloses a method for quickly calculating the axial force of a permanent magnet coupler, belongs to the technical field of permanent magnet eddy current speed regulation, and relates to a method for quickly calculating the axial force of the permanent magnet coupler. The method fully considers the actual structure of the permanent magnet coupler, firstly, an equivalent linear model of the permanent magnet coupler is established according to the basic size of a permanent magnet, and the effective area of the permanent magnet coupler under the action of axial force is calculated; calculating the magnetic resistance and leakage magnetic resistance of each part on the path through the path of the magnetic force line of the permanent magnet coupler to obtain the effective magnetic induction intensity of the axial force action of the permanent magnet coupler; and obtaining a calculation result of the axial force of the permanent magnet coupler according to the effective energy of the axial force action of the permanent magnet coupler. The method gets rid of the limitation and the complexity of the traditional finite element method, quickly calculates the axial force in the normal operation process of the permanent magnet coupler, and greatly improves the calculation speed of the axial force of the permanent magnet coupler. The method has universality, convenient operation and simple flow in practical engineering application.
Description
Technical Field
The invention belongs to the technical field of permanent magnet eddy current speed regulation, and relates to a method for quickly calculating the axial force of a permanent magnet coupler.
Background
Along with the high-speed development of energy industries such as petrifaction and coal-electricity, high-speed heavy-duty equipment in the energy field puts higher energy-saving requirements on a speed regulating device of the high-speed heavy-duty equipment. The permanent magnet coupler is used as a non-contact speed regulating device, and can effectively reduce energy consumption and improve economic benefit due to the characteristics of reliable operation, long service life, remarkable energy-saving effect and the like, so that the permanent magnet coupler is widely applied to high-speed heavy-load equipment. Axial force must be considered in the assembly process of the permanent magnet coupler, otherwise axial movement of the conductor rotor and the permanent magnet rotor can be caused during operation, the service life of connecting pieces such as bearings is further influenced, and even safety accidents such as personal injury can occur. At present, the rapid calculation method for the axial force of the permanent magnet coupler is mainly finite element calculation, the finite element calculation method is long in time consumption, complicated in model structure construction process and not simple and convenient to operate.
Aiming at the research of the axial force of the permanent magnet coupler, the inventor's axial permanent magnet eddy current coupler transmission performance analysis' is published in 2016 in the 12 th period of scientific innovation and productivity by tai yuan research institute of coal science and industry group, and a simulation model is established for the permanent magnet coupler, the rule that the axial force of the permanent magnet coupler changes along with the slip is analyzed through a finite element calculation method, the structure of the permanent magnet coupler is simplified during simulation modeling, the calculation steps are complex, and the simulation result is interfered by factors such as the number of grids, the type of the grids, the step value and the like, so that the axial force of the permanent magnet coupler in the normal operation process cannot be rapidly calculated. Therefore, it is very necessary to provide a fast calculation method for the axial force of the permanent magnet coupler.
Disclosure of Invention
The invention aims to make up for the defects of the prior art, and provides a method for quickly calculating the axial force of a permanent magnet coupler, which aims to calculate the axial force of the permanent magnet coupler used by high-speed heavy-load equipment more quickly and simply, so that the accuracy of the model selection of a shaft end connecting piece and the safety of the operation of the permanent magnet coupler are ensured. The method focuses on the actual structure of the permanent magnet coupler, overcomes the limitation of the traditional finite element method, solves the inconvenience of the traditional method for calculating the axial force of the permanent magnet coupler, and greatly improves the calculation speed of the axial force of the permanent magnet coupler. The method has universality in practical engineering application, is convenient to operate and has a simple process.
The technical scheme adopted by the invention is a rapid calculation method for the axial force of a permanent magnet coupler, which is characterized in that the method fully considers the actual structure of the permanent magnet coupler, firstly, an equivalent straight line model of the permanent magnet coupler is established according to the basic size of a permanent magnet, and the effective area of the permanent magnet coupler under the action of the axial force is calculated; calculating the magnetic resistance and leakage magnetic resistance of each part on the path through the path of the magnetic force line of the permanent magnet coupler to obtain the effective magnetic induction intensity of the axial force action of the permanent magnet coupler; and obtaining a calculation result of the axial force of the permanent magnet coupler according to the effective energy of the axial force action of the permanent magnet coupler. The test method comprises the following specific steps:
firstly, calculating the effective area of the axial force action of the permanent magnet coupler
According to the basic size of the permanent magnet 3, the number of pole pairs p of the permanent magnet and the inner diameter rm of the permanent magnet are included1Outer diameter rm of permanent magnet2Bottom width b of permanent magnet1Width of permanent magnet top b2Calculating the average radius rm of the permanent magnet 30Comprises the following steps:
rm0＝(rm1+rm2)/2 (1)
the radial length L of the permanent magnet 3 is further calculated as:
L＝rm2-rm1 (2)
for ease of calculation and intuitive understanding, the average radius rm of the permanent magnet coupler along the permanent magnet 3 is determined0Unfolding, establishing an equivalent linear model of the permanent magnet coupler, and calculating the effective area S of the single permanent magnet under the action of axial forceeComprises the following steps:
Se＝0.5(b1+b2)L (3)
calculating the effective area S of the permanent magnet coupler under the action of axial forcetotalComprises the following steps:
Stotal＝2pK1Se (4)
in the formula (4), K1Is the effective area correction factor.
Secondly, calculating the effective magnetic induction intensity of the axial force action of the permanent magnet coupler
The path of the magnetic force lines of the permanent magnet coupler passes through the permanent magnet 3, enters the permanent magnet air gap 5, the copper conductor disc 2 and the iron guide disc 1, then passes through the magnet disc 4 and returns to the permanent magnet 3, and the magnetic force lines form a closed path.
For the magnetic resistance R existing at the iron guide disc 11Obtained from equation (5):
R1＝l1/(μ1Se) (5)
in the formula (5), l1Thickness of the iron guide plate 1, μ1The relative permeability of the iron conductive disc 1.
For the magnetic resistance R existing at the copper conductor disc 22Obtained from equation (6):
R2＝l2/(μ2Se) (6)
in the formula (6), l2Is the thickness, mu, of the copper conductor plate 22Is the relative permeability of the copper conductor disc 2.
Magnetic resistance R existing at permanent magnet 33Comprises the following steps:
R3＝l3/(μ3Se) (7)
in the formula (7), l3Is the thickness, mu, of the permanent magnet 33Is the relative permeability of the permanent magnet 3.
Magnetic resistance R existing at the magnet disk 44Comprises the following steps:
R4＝l4/(μ4Se) (8)
in the formula (8), l4Is the thickness of the magnet disk 4, mu4Is the relative permeability of the magnet disc 4.
Reluctance R present at the permanent magnet air gap 55Comprises the following steps:
R5＝l5/(μ5Se) (9)
in the formula (9), l5Thickness of the permanent magnet air gap 5, mu5Is the relative permeability of the permanent magnetic air gap 5.
Leakage magnetic resistance RX exists at the permanent magnet air gap 50Including leakage reluctance between permanent magnetsRX1And leakage reluctance RX of the permanent magnet body2The specific calculation formula is as follows:
in the formula (10), b3Is the average spacing between adjacent permanent magnets.
Leakage reluctance RX at the permanent magnet air gap 50Is composed of
RX0＝RX1+RX2 (11)
The permanent magnet 3 is used as a power source of a magnetic field and is responsible for providing magnetic potential F3The magnitude of which is determined by the coercive force H of the permanent magnet 33And the thickness l of the permanent magnet 33The determination and calculation formula is as follows
F3＝K3H3l3 (12)
In the formula (12), K3Is a magnetic potential correction coefficient.
Further calculating the effective magnetic flux phi of the permanent magnet coupler under the action of axial forceeComprises the following steps:
the magnetic induction intensity and the magnetic flux have a linear relation, and the effective magnetic induction intensity B of the axial force action of the permanent magnet coupler is further obtainedeComprises the following steps:
Be＝φe/Se (14)
thirdly, obtaining the calculation result of the axial force of the permanent magnet coupler
In the normal operation process of the permanent magnet coupler, the permanent magnet air gap 5 between the copper conductor disc 2 and the permanent magnet 3 is very small, so that the effective magnetic induction intensity B of the axial force action of the permanent magnet coupler in the small-range areaeEffective energy W of axial force action of permanent magnet coupler considered as uniformeComprises the following steps:
We＝Be 2l5Stotal/(2μ5) (15)
obtaining the axial force F of the permanent magnet couplereComprises the following steps:
Fe＝Be 2Stotal/(2μ5) (16)
according to the axial force F of the permanent magnet couplereThe calculation result can guide the model selection work of the permanent magnet coupler shaft end connecting bearing. In order to ensure the operation safety of the permanent magnet coupler, the maximum axial force F endured by the shaft end connecting bearing is selectedmaxThe following conditions must be satisfied
Fmax≥1.2Fe (17)
At this point, the rapid calculation of the permanent magnet coupler axial force is completed.
The method has the advantages that the effective area of the permanent magnet coupler under the action of the axial force is calculated according to the basic size of the permanent magnet, the actual structure of the permanent magnet coupler is fully considered, the magnetic resistance and the leakage magnetic resistance of each part on the path are considered, and the accuracy of the calculation result of the axial force of the permanent magnet coupler is ensured. The limitation and the complexity of the traditional finite element method are eliminated, the axial force of the permanent magnet coupler in the normal operation process is quickly calculated, and the axial force calculation speed of the permanent magnet coupler is greatly improved. The method is convenient to operate and simple in process in practical engineering application, and is a calculation method with engineering universality and convenience.
Drawings
Fig. 1 is a flow chart of a method for rapidly calculating an axial force of a permanent magnet coupler.
Fig. 2 is a schematic structural diagram of a permanent magnet coupler, and fig. 3 is a schematic equivalent straight line model diagram of the permanent magnet coupler. The magnetic-field-type permanent magnet synchronous motor comprises a 1-iron conducting disc, a 2-copper conductor disc, a 3-permanent magnet, a 4-magnet disc and a 5-permanent magnet air gap.
Detailed Description
The embodiments of the present invention will be further explained with reference to the drawings and technical solutions
In the embodiment, a 6-pole pair and 45KW rated permanent magnet coupler axial force is selected for calculation.
Wherein6 permanent magnet pole pair number p of permanent magnet coupler with 6 poles and rated power of 45KW and permanent magnet inner diameter rm1105mm, permanent magnet outer diameter rm2155mm, permanent magnet base width b140mm, width of permanent magnet top b260mm, effective area correction factor K1Thickness l of the iron guide plate of 0.251Relative magnetic permeability mu of iron-conductive disc of 12mm1Thickness l of copper conductor disc 20002Relative permeability mu of a 5mm, copper conductor disc20.999995 thickness l of permanent magnet325mm, relative permeability μ of permanent magnet3Thickness l of the magnet disc 1.1410mm, relative permeability μ of the magnet disc41800 thickness l of permanent magnet air gap54mm, relative permeability mu of permanent magnet air gap5＝4π×10-7Average distance b between adjacent permanent magnets3Coercive force H of permanent magnet of 19mm3860KA/m, magnetic potential correction coefficient K3＝0.086。
A flow chart of a method for rapidly calculating an axial force of a permanent magnet coupler, as shown in fig. 1. The specific steps of the calculation method are as follows:
firstly, calculating the effective area of the axial force action of the permanent magnet coupler
According to the basic size of the permanent magnet 3, the number of pole pairs p of the permanent magnet and the inner diameter rm of the permanent magnet are included1Outer diameter rm of permanent magnet2Bottom width b of permanent magnet1Width of permanent magnet top b2The average radius rm of the permanent magnet 3 is calculated from the formula (1)0130 mm; the radial length L of the permanent magnet 3 was further calculated to be 50 mm.
For ease of calculation and intuitive understanding, the average radius rm of the permanent magnet coupler along the permanent magnet 3 is determined0Unfolding, establishing an equivalent linear model of the permanent magnet coupler, and calculating the effective area S of the single permanent magnet under the action of axial force according to the formula (3)e＝2500mm2。
Further calculating the effective area S of the permanent magnet coupler under the action of axial force by the formula (4)total＝7500mm2。
Secondly, calculating the effective magnetic induction intensity of the axial force action of the permanent magnet coupler
The path of the magnetic force lines of the permanent magnet coupler passes through the permanent magnet 3, enters the permanent magnet air gap 5, the copper conductor disc 2 and the iron guide disc 1, then passes through the magnet disc 4 and returns to the permanent magnet 3, and the magnetic force lines form a closed path.
For the magnetic resistance R existing at the iron guide disc 11R is obtained by calculation of the formula (5)1＝0.0024H-1(ii) a For the magnetic resistance R existing at the copper conductor disc 22R is obtained by calculation of the formula (6)2＝2H-1(ii) a For the reluctance R existing at the permanent magnet 33R is obtained by calculation of the formula (7)3＝9.0909H-1(ii) a For the magnetic resistance R existing at the magnet disc 44R is obtained by calculation of the formula (8)4＝0.0022H-1(ii) a For the reluctance R present at the permanent magnetic air gap 55R is obtained by calculation of the formula (9)5＝1.27×106H-1。
Leakage magnetic resistance RX exists at the permanent magnet air gap 50Including leakage reluctance RX between permanent magnets1And leakage reluctance RX of the permanent magnet body2RX is obtained by calculation of equation (10)1＝9.85×107H-1And RX2＝2.37×108H-1(ii) a The leakage reluctance RX at the permanent magnet air gap 5 is further obtained by equation (11)0＝3.36×108H-1
The permanent magnet 3 is used as a power source of a magnetic field and is responsible for providing magnetic potential F3The magnitude of which is determined by the coercive force H of the permanent magnet 33And the thickness l of the permanent magnet 33Determining that F is calculated from the formula (12)3＝15480A。
Further, the effective magnetic flux phi of the permanent magnet coupler under the action of axial force is calculated by the formula (13)e0.0243 Wb; the magnetic induction intensity and the magnetic flux have a linear relation, and the effective magnetic induction intensity B of the permanent magnet coupler under the action of axial force is further obtained by the formula (14)e＝1.16T。
Thirdly, obtaining the calculation result of the axial force of the permanent magnet coupler
During normal operation of the permanent magnet coupler, the permanent magnet air gap 5 between the copper conductor disc 2 and the permanent magnet 3 is small, and therefore, in this caseEffective magnetic induction intensity B of axial force action of permanent magnet coupler in small-range areaeThe effective energy W of the axial force of the permanent magnet coupler is calculated from equation (15) and considered to be uniforme16.11N · m; further obtaining the axial force F of the permanent magnet coupler by the formula (16)e＝4028N。
According to the axial force F of the permanent magnet couplereThe calculation result can guide the model selection work of the permanent magnet coupler shaft end connecting bearing. In order to ensure the safe operation of the permanent magnet coupler, the maximum axial force F endured by the shaft end connecting bearing is selected by the formula (17)maxMust satisfy Fmax≥4834N。
The rapid calculation method of the invention calculates the effective area of the permanent magnet coupler under the action of the axial force according to the basic size of the permanent magnet, fully considers the actual structure of the permanent magnet coupler, simultaneously considers the magnetic resistance of each part on the path and the leakage magnetic resistance, and ensures the correctness of the calculation result of the axial force of the permanent magnet coupler. The method gets rid of the limitation and the complexity of the traditional finite element method, quickly calculates the axial force in the normal operation process of the permanent magnet coupler, and is a calculation method with engineering universality and convenience.
Claims (1)
1. A fast calculation method of the axial force of a permanent magnet coupler is characterized in that the method fully considers the actual structure of the permanent magnet coupler, firstly, an equivalent straight line model of the permanent magnet coupler is established according to the basic size of a permanent magnet, and the effective area of the permanent magnet coupler under the action of the axial force is calculated; calculating the magnetic resistance and leakage magnetic resistance of each part on the path through the path of the magnetic force line of the permanent magnet coupler to obtain the effective magnetic induction intensity of the axial force action of the permanent magnet coupler; obtaining a calculation result of the axial force of the permanent magnet coupler according to the effective energy of the axial force action of the permanent magnet coupler; the specific steps of the calculation method are as follows:
firstly, calculating the effective area of the axial force action of the permanent magnet coupler
According to the basic size of the permanent magnet (3), the number of the pole pairs p of the permanent magnet and the inner diameter rm of the permanent magnet are included1Outer diameter rm of permanent magnet2Bottom width b of permanent magnet1Width of permanent magnet top b2Calculating the average radius rm of the permanent magnet (3)0Comprises the following steps:
rm0＝(rm1+rm2)/2 (1)
further calculating the radial length L of the permanent magnet (3) as follows:
L＝rm2-rm1 (2)
the permanent magnet coupler is arranged along the average radius rm of the permanent magnet (3)0Unfolding, establishing an equivalent linear model of the permanent magnet coupler, and calculating the effective area S of the single permanent magnet under the action of axial forceeComprises the following steps:
Se＝0.5(b1+b2)L (3)
calculating the effective area S of the permanent magnet coupler under the action of axial forcetotalComprises the following steps:
Stotal＝2pK1Se (4)
in the formula (4), K1Is the effective area correction factor;
secondly, calculating the effective magnetic induction intensity of the axial force action of the permanent magnet coupler
The path of the magnetic force line of the permanent magnet coupler passes through the permanent magnet (3), enters the permanent magnet air gap (5), the copper conductor disc (2) and the iron guide disc (1), then passes through the magnet disc (4) and returns to the permanent magnet (3), namely the magnetic force line forms a closed path;
for the magnetic resistance R existing at the iron guide disc (1)1Obtained from equation (5):
R1＝l1/(μ1Se) (5)
in the formula (5), l1Is the thickness of the iron guide plate (1) [ mu ]1Is the relative magnetic permeability of the iron guide disc (1);
for the magnetic resistance R existing at the copper conductor disc (2)2Obtained from equation (6):
R2＝l2/(μ2Se) (6)
in the formula (6), l2Is the thickness of the copper conductor plate (2) [ mu ]2Is the relative magnetic permeability of the copper conductor disc (2);
magnetic resistance R existing at the permanent magnet (3)3Comprises the following steps:
R3＝l3/(μ3Se) (7)
in the formula (7), l3Is the thickness of the permanent magnet (3) < mu >3Is the relative permeability of the permanent magnet (3);
magnetic resistance R existing at the magnet disc (4)4Comprises the following steps:
R4＝l4/(μ4Se) (8)
in the formula (8), l4Is the thickness of the magnet disc (4), mu4Is the relative magnetic permeability of the magnet disc (4);
reluctance R existing at the permanent magnet air gap (5)5Comprises the following steps:
R5＝l5/(μ5Se) (9)
in the formula (9), l5Is the thickness of the permanent magnet air gap (5) [ mu ]5Is the relative magnetic permeability of the permanent magnetic air gap (5);
leakage magnetic resistance RX exists at the position of the permanent magnet air gap (5)0Including leakage reluctance RX between permanent magnets1And leakage reluctance RX of the permanent magnet body2The specific calculation formula is as follows:
in the formula (10), b3Is the average spacing between adjacent permanent magnets;
leakage reluctance RX at the permanent magnet air gap (5)0Comprises the following steps:
RX0＝RX1+RX2 (11)
the permanent magnet (3) is used as a power source of a magnetic field and is responsible for providing magnetic potential F3The magnitude of which is determined by the coercive force H of the permanent magnet (3)3And the thickness l of the permanent magnet (3)3And determining, wherein the calculation formula is as follows:
F3＝K3H3l3 (12)
in the formula (12), K3The magnetic potential correction coefficient;
further calculating the effective magnetic flux phi of the permanent magnet coupler under the action of axial forceeComprises the following steps:
the magnetic induction intensity and the magnetic flux have linear relation, so the effective magnetic induction intensity B of the axial force action of the permanent magnet couplereComprises the following steps:
Be＝φe/Se (14)
thirdly, obtaining the calculation result of the axial force of the permanent magnet coupler
Effective magnetic induction intensity B of axial force action of the permanent magnet coupler in the normal operation process of the permanent magnet couplereEffective energy W of axial force action of permanent magnet coupler considered as uniformeComprises the following steps:
We＝Be 2l5Stotal/(2μ5) (15)
obtaining the axial force F of the permanent magnet couplereComprises the following steps:
Fe＝Be 2Stotal/(2μ5) (16)
according to the axial force F of the permanent magnet couplereThe calculation result of the model selection guide module guides the model selection work of the permanent magnet coupler shaft end connecting bearing; in order to ensure the operation safety of the permanent magnet coupler, the maximum axial force F endured by the shaft end connecting bearing is selectedmaxThe following conditions must be satisfied:
Fmax≥1.2Fe (17)
at this point, the rapid calculation of the permanent magnet coupler axial force is completed.
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| US7252112B1 (en) * | 2006-06-01 | 2007-08-07 | Catlow, Inc. | Breakaway hose coupling with a magnetic connection |
| CN104682661A (en) * | 2015-03-10 | 2015-06-03 | 盐城华力达科技有限公司 | Permanent magnet coupler |
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