CN112329293B - Calculation method for no-load counter potential and thrust of permanent magnet linear synchronous motor - Google Patents
Calculation method for no-load counter potential and thrust of permanent magnet linear synchronous motor Download PDFInfo
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- H—ELECTRICITY
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Abstract
The invention provides a calculation method for no-load counter potential and thrust of a permanent magnet linear synchronous motor, which comprises the following steps: firstly, constructing an air gap field analysis model of a slotless permanent magnet linear motor, and obtaining the slotless magnetic flux density of an air gap region through a separation variable method and boundary conditions; secondly, constructing an improved two-dimensional air gap relative flux guide function of the permanent magnet linear motor by taking a groove as an analysis model, and calculating the normal and tangential air gap flux densities when the permanent magnet linear motor is grooved; then, calculating the empty load flux density of an air gap area according to the air gap flux density and the improved two-dimensional air gap relative flux guide function, and calculating the flux linkage generated by a single-turn coil by the empty load flux density so as to further calculate the empty load counter potential generated by a one-phase winding; and finally, calculating the thrust of the permanent magnet linear motor according to the no-load counter potential, and verifying the correctness of the calculation method by using a finite element. The method is suitable for electromagnetic parameter calculation of the integer slot and fractional slot motors on the premise of ensuring accuracy, and has the characteristics of simplicity and convenience in solving, small calculated amount and good universality.
Description
Technical Field
The invention relates to the technical field of permanent magnet linear motors, in particular to a calculation method for no-load back electromotive force and thrust of a permanent magnet linear synchronous motor.
Background
The permanent magnet linear synchronous motor combines the structural characteristics of the permanent magnet synchronous motor and the linear motor, has the advantages of high thrust density, high positioning precision, good reliability and the like, has obvious application advantages in the linear motion fields of high-speed logistics, wireless elevator direct drive systems, numerical control machine tool systems, rail transit linear traction systems and the like, and has become a research hot spot for domestic and foreign scholars and scientific research institutions in recent years.
The no-load counter potential and the thrust of the permanent magnet linear synchronous motor are important parameters for analyzing the performance of the motor, and an analytic method and a finite element method are often adopted to calculate the counter potential and the thrust of the motor. Compared with the finite element method, the analytic method has visual physical concept and high calculation speed. The finite element method can accurately solve the magnetic field of the complex motor structure, has good universality, but the processing modeling and the post-processing solving are long in time consumption, cannot intuitively reflect the rule of influence of design parameters on motor performance, has low efficiency in parameterized calculation of the motor structure, and is commonly used for verifying the correctness of the analysis result. The resolving of the no-load counter potential and the thrust mainly comprises the following steps: magnetic circuit method, equivalent magnetic network method, angle-preserving transformation method, and accurate subdomain method. The magnetic circuit method adopts a method of field-based path, some centralized parameters are related to empirical coefficients, and the calculation accuracy of electromagnetic parameters is very low. The equivalent magnetic network method can solve the influence of magnetic circuit saturation and magnetic leakage on electromagnetic parameters, but the method is similar to finite element mesh subdivision, and modeling workload is increased along with the increase of nodes, so that the calculation efficiency is low. The angle-preserving transformation method is used for analyzing the no-load counter potential and thrust, the accuracy is high, but the calculation is complex after multiple plane transformations are needed. The no-load counter potential and the thrust are solved by adopting an accurate subdomain method, the calculated result is basically consistent with the finite element result, but the boundary condition is complicated to process, the formula is numerous and not intuitive, and the calculation workload is great. The common feature of the above methods is that the air gap magnetic field is calculated first and then other electromagnetic parameters are obtained.
Unlike the current complex air gap relative flux guide solving magnetic field, the complex air gap relative flux guide solving magnetic field is obtained by utilizing the mathematical rule of magnetic field divergence near the tooth top corner area, combining boundary conditions of notch areas and utilizing a Carlsberg coefficient, so that the complexity of the flux density solving process is reduced, the complex air gap relative flux guide solving magnetic field has a plurality of advantages, but an integral term exists in an expression of the complex air gap relative flux guide solving magnetic field, and the solving time is increased in solving no-load counter potential and thrust. The two-dimensional air gap relative flux guide function can be used for solving an air gap magnetic field, the expression is a parameter summation term, if the electromagnetic parameter can be solved by using the two-dimensional air gap relative flux guide function, the calculation efficiency can be further improved, the calculation of the electromagnetic parameter is convenient, no-load counter potential and no-load thrust of a motor are solved by using the two-dimensional air gap relative flux guide function at present, and the two reasons are mainly as follows: firstly, the current two-dimensional air gap relative flux guiding function only considers the normal component, but not the tangential component, and the improvement is needed, and secondly, the solving of the magnetic flux after the air gap flux density is obtained through the two-dimensional air gap relative flux guiding function is difficult, so that the space-borne counter potential and the thrust are difficult to solve. If the two problems can be solved, the no-load counter potential and the thrust of the motor can be directly solved by utilizing the two-dimensional air gap relative flux guide function, compared with the method, the method can greatly simplify the current complex analytical calculation, improve the calculation efficiency and is an effective and convenient calculation method.
Disclosure of Invention
Aiming at the defects in the background art, the invention provides a method for calculating the no-load counter potential and the thrust of the permanent magnet linear synchronous motor, and solves the technical problem of higher calculation complexity of the no-load counter potential and the thrust of the conventional permanent magnet linear synchronous motor.
The technical scheme of the invention is realized as follows:
a method for calculating no-load counter potential and thrust of a permanent magnet linear synchronous motor comprises the following steps:
step one: constructing an air gap field analysis model of the slotless permanent magnet linear motor, and obtaining the slotless magnetic flux density of an air gap region through a separation variable method and boundary conditions;
step two: taking a groove as an analysis model, selecting the center of the groove as an origin, constructing a normal two-dimensional air gap relative flux guiding function and a tangential two-dimensional air gap relative flux guiding function when the permanent magnet linear motor is grooved, and constructing an improved two-dimensional air gap relative flux guiding function of the permanent magnet linear motor by the normal two-dimensional air gap relative flux guiding function and the tangential two-dimensional air gap relative flux guiding function;
step three: calculating the normal air gap flux density and the tangential air gap flux density of the permanent magnet linear motor during slotting according to the improved two-dimensional air gap relative flux guiding function in the second step;
step four: calculating the empty load flux density of an air gap area when the permanent magnet linear motor is grooved according to the air gap flux density of the first step and the improved two-dimensional air gap relative flux guiding function, calculating the flux linkage generated by a single-turn coil according to the empty load flux density, and calculating the empty load counter potential generated by a one-phase winding according to the flux linkage generated by the single-turn coil;
step five: and (3) calculating the thrust of the permanent magnet linear motor according to the no-load counter potential in the step four, and verifying the correctness of the no-load counter potential and the thrust of the integer slot and the fractional slot permanent magnet linear motor by using a finite element.
The air gap field analysis model of the slotless permanent magnet linear motor is as follows:
wherein A is z2 (x, y) is the vector magnetic potential of the permanent magnet region, A z3 (x, y) is the vector magnetic potential of the air gap region,k＝π/τ，M 0 ＝B r /μ 0 ，M 0 is the magnetic pole magnetization intensity, B r Mu, the residual magnetism of the magnetic pole 0 Is air permeability, a p ＝L m /τ，L m Is long in magnetic pole and τ is pole pitch.
The boundary conditions are:
wherein h is m Is of permanent magnet height, delta is the length of the air gap, B 2x Is the normal magnetic density of the magnetic pole area, B 3x Is the normal magnetic density of the air gap area, B 2y Is the tangential magnetic density of the magnetic pole area, B 3y Tangential magnetic density of the air gap area;
the air gap area slotless magnetic flux density obtained by the separation variable method and the boundary condition is as follows:
wherein B is 3xnos (x, y) represents the tangential slotless flux density of the air gap region, B 3ynos (x, y) represents the normal ungrooved flux density of the air gap region.
The relative flux guide function of the normal two-dimensional air gap when the permanent magnet linear motor is grooved is as follows:
the tangential two-dimensional air gap relative flux guide function when the permanent magnet linear motor is grooved is as follows:
wherein lambda is y (x, y) is the normal two-dimensional air gap relative flux guide, lambda x (x, y) is tangential two-dimensional air gap relative flux guide, a 0 For the distance of the slot centerline from the a-phase winding axis, z=2pi/t s ，t s Is tooth pitch, b s In order to be a groove width, beta (y) is a nonlinear function.
The improved two-dimensional air gap relative flux guide function of the permanent magnet linear motor is as follows:
λ r (x,y)＝λ y (x,y)+jλ x (x,y)
wherein lambda is r And (x, y) is the two-dimensional air gap relative flux guide of the permanent magnet linear motor.
The method for calculating the normal air gap flux density and the tangential air gap flux density of the permanent magnet linear motor during slotting according to the improved two-dimensional air gap relative flux guide function in the second step comprises the following steps:
calculating the flux density of the slotted air gap:
B s (x,y)＝B nos (x,y)·λ r * (x,y)
wherein B is s (x, y) is the magnetic density with grooves, B nos (x, y) is the magnetic density without groove, lambda r * (x, y) is the complex conjugate of the two-dimensional air gap relative flux guide;
writing the slotted magnetic density and the ungrooved magnetic density into a complex form:
B s (x,y)＝B ys (x,y)+jB xs (x,y)
B nos (x,y)＝B ynos (x,y)+jB xnos (x,y)
wherein B is ys (x, y) is the normal magnetic density of the grooved magnetic density, B xs (x, y) is tangential magnetic flux density of grooved magnetic flux density, B ynos (x, y) is the normal magnetic density of the slotless magnetic density, B xnos (x, y) is tangential magnetic density of the slotless magnetic density;
calculating the normal air gap flux density and the tangential air gap flux density of the permanent magnet linear motor during slotting according to the improved two-dimensional air gap relative flux guiding function, the slotted flux density and the ungrooved flux density:
B ys (x,y)＝B ynos (x,y)·λ y (x,y)+B xnos (x,y)·λ x (x,y)
B xs (x,y)＝B xnos (x,y)·λ y (x,y)-B ynos (x,y)·λ x (x,y)
wherein B is ys (x, y) is the normal air gap flux density when the permanent magnet linear motor is grooved, B xs And (x, y) is tangential air gap flux density when the permanent magnet linear motor is grooved.
The empty magnetic density of the air gap area when the permanent magnet linear motor is grooved is as follows:
B 3ys (x,y)＝B 3ynos (x,y)·λ y (x,y)+B 3xnos (x,y)·λ x (x,y)
B 3xs (x,y)＝B 3xnos (x,y)·λ y (x,y)-B 3ynos (x,y)·λ x (x,y)
wherein B is 3ys (x, y) represents the tangential slotted flux density of the air gap region, B 3xs (x, y) represents the magnetic flux density of the grooves normal to the air gap region;
the magnetic linkage psi generated by the single-turn coil c The method comprises the following steps:
wherein L is a For the length of the iron core, a y ＝y 1 t s For coil pitch, y 1 Is the number of slots spanned by the coil.
The one-phase winding generatesIdle counter potential E of (2) φ The method comprises the following steps:
wherein N is 1 For each phase winding series turns, phase A theta 0 =0, b phase θ 0 =2pi/3, phase c θ 0 ＝4π/3，k dn In order to distribute the coefficients of the power distribution,for the slot opening coefficient, v 1 For the speed of the motor rotor, B yn (n) is the Fourier coefficient, B xn (n) is the Fourier coefficient, when y 1 Odd number of grooves, then a 0 ＝t s /2，cos(mza 0 ) Cos (mpi), when y 1 An even number of slots, then a 0 ＝0，cos(mza 0 )＝1。
Thrust force F of permanent magnet linear motor x The method comprises the following steps:
wherein p is e Representing the electromagnetic power of the motor E a 、E b 、E c The no-load counter potential of the A, B, C phase is shown, a, B, C three-phase currents are respectively adopted, and I is a current effective value.
The technical scheme has the beneficial effects that: in order to simplify the calculation complexity of the no-load counter potential and the thrust of the existing permanent magnet linear synchronous motor and improve the calculation efficiency of an analytical model, the invention adopts an improved two-dimensional air gap relative flux guide function so as to calculate the no-load counter potential and the thrust of the motor when the tooth slot effect is considered. Firstly, a slotless PMLSM analytical model is established, an improved two-dimensional air gap relative flux guide function is provided to solve the problem of tangential air gap relative flux guide distribution, and the air gap flux density normal direction and tangential distribution during motor slotting are calculated according to the slotted permanent magnet linear synchronous motor analytical model. The air gap is densified into a Fourier series form, no-load counter potential and thrust of the motor under the coordination of different pole slots are obtained according to the flux linkage of the winding, the influence of the pole slot coordination, different slot widths and winding distribution on electromagnetic parameters is discussed, and the accuracy of an analysis method is proved by a finite element method. The method is suitable for calculating the electromagnetic parameters of the integer slot permanent magnet linear synchronous motor and the fractional slot permanent magnet linear synchronous motor on the premise of ensuring accuracy, has the characteristics of simple and convenient solving method, small calculated amount and good universality, is favorable for quick electromagnetic design and performance optimization of the motor, and is a very effective electromagnetic parameter calculating method.
Drawings
In order to more clearly illustrate the embodiments of the invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, it being obvious that the drawings in the following description are only some embodiments of the invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a schematic flow chart of the present invention.
Fig. 2 is a magnetic field analysis model of a slotless permanent magnet linear motor.
FIG. 3 is a two-dimensional air gap relative flux guide distribution for an 18-slot 6-pole half-closed slot improvement.
FIG. 4 is a two-dimensional air gap relative flux guide distribution for an 18-slot 6-pole rectangular slot improvement.
FIG. 5 is a two-dimensional air gap relative flux guide distribution for a 12-slot 14-pole half-closed slot improvement.
FIG. 6 is a two-dimensional air gap relative flux guide distribution for a 12-slot 14-pole rectangular slot improvement.
Figure 7 integer tank 18 tank 6 half-closed tank no-load counter potential waveform.
Fig. 8 is an integer slot 18 slot 6 polar rectangular slot no-load counter potential waveform.
Fig. 9 shows the no-load counter potential waveform of the fractional tank 12 tank 14 extremely semi-closed tank.
Fig. 10 shows the fractional slot 12 slot 14 polar rectangular slot no-load counter potential waveform.
Fig. 11 shows an integer groove 18 groove 6-pole half-closed groove thrust waveform.
Fig. 12 shows the integer slot 18 slot 6 polar rectangular slot thrust waveform.
Fig. 13 shows a very semi-closed slot thrust waveform for the fractional slot 12 slot 14.
Fig. 14 shows the fractional slot 12 slot 14 polar rectangular slot thrust waveform.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without any inventive effort, are intended to be within the scope of the invention.
As shown in fig. 1, the embodiment of the invention provides a method for calculating no-load counter potential and thrust of a permanent magnet linear synchronous motor, which comprises the following steps: neglecting end effects, the magnetic permeability of the permanent magnet is the same in all directions and equal to the air magnetic permeability; the magnetic conductivity of the stator core is infinity, and the magnetic circuit is unsaturated; neglecting adjacent cogging, the stator slots are infinitely deep. Based on the assumption, a slotless PMLSM magnetic field layering model is established, and as shown in figure 2, the model is divided into four solving areas of 1, 2, 3 and 4, which correspond to the stator yoke, the permanent magnet, the air gap and the rotor yoke area respectively. The method comprises the following specific steps:
step one: constructing an air gap field analysis model of the slotless permanent magnet linear motor, and obtaining the slotless magnetic flux density of an air gap region through a separation variable method and boundary conditions;
vector magnetic position A is used for air gap magnetic field analytic model of slotless permanent magnet linear motor z (x, y) is a solution variable, the permanent magnet area is poisson equation, and the air gap area is Laplacian equation:
wherein A is z2 (x, y) is the vector magnetic potential of the permanent magnet region, A z3 (x, y) is the vector magnetic potential of the air gap region,k＝π/τ，M 0 ＝B r /μ 0 ，M 0 is the magnetic pole magnetization intensity, B r Mu, the residual magnetism of the magnetic pole 0 Is air permeability, a p ＝L m /τ，L m Is long in magnetic pole and τ is pole pitch.
The magnetic field boundary conditions of the air gap region and the magnetic pole region are as follows:
wherein h is m Is of permanent magnet height, delta is the length of the air gap, B 2x Is the normal magnetic density of the magnetic pole area, B 3x Is the normal magnetic density of the air gap area, B 2y Is the tangential magnetic density of the magnetic pole area, B 3y Tangential magnetic density of the air gap area;
according to formulas (1), (2) and (3), the air gap area slotless magnetic density obtained by the separation variable method and the boundary condition is:
wherein B is 3xnos (x, y) represents the tangential slotless flux density of the air gap region, B 3ynos (x, y) represents the normal ungrooved flux density of the air gap region.
Step two: taking a groove as an analysis model, selecting the center of the groove as an origin, constructing a normal two-dimensional air gap relative flux guiding function and a tangential two-dimensional air gap relative flux guiding function when the permanent magnet linear motor is grooved, and constructing an improved two-dimensional air gap relative flux guiding function of the permanent magnet linear motor by the normal two-dimensional air gap relative flux guiding function and the tangential two-dimensional air gap relative flux guiding function;
taking a groove as an analysis model, selecting the center of the groove as an origin, and adopting a gram-gram transformation method, wherein the expression of a normal two-dimensional air gap relative flux guide function of the permanent magnet linear motor is as follows:
the equation (5) contains a constant term and a cosine series term, the relative flux-guide distribution of the two-dimensional air gap in the tangential direction is an even function, the relative flux-guide distribution of the two-dimensional air gap in the tangential direction is symmetrical about the center line of the groove, only the influence of the cogging effect on the relative flux-guide distribution of the air gap in the normal direction can be considered, a detailed analytical formula is not shown in the literature at present for the influence in the tangential direction, the relative flux-guide distribution of the air gap in the tangential direction is an odd function, therefore, the relative flux-guide of the air gap in the tangential direction has no constant term, the relative flux-guide distribution of the air gap in the tangential direction has similarity with the harmonic amplitude in the normal direction, and the relative flux-guide expression of the two-dimensional air gap in the tangential direction can be obtained approximately:
wherein lambda is y (x, y) is the normal two-dimensional air gap relative flux guide, lambda x (x, y) is tangential two-dimensional air gap relative flux guide, a 0 For the distance of the slot centerline from the a-phase winding axis, z=2pi/t s ，t s Is tooth pitch, b s In order to be a groove width, beta (y) is a nonlinear function and is related to the groove width, the distance between fixed sub-elements and the position of the air gap, and is used for determining the magnitude of each subharmonic of the relative flux guide of the air gap.
Equations (5) and (6) constitute an improved two-dimensional air gap relative flux guide function. To obtain air gap flux density considering cogging effect, an improved two-dimensional air gap relative flux guide function lambda r (x, y) is written in the form:
λ r (x,y)＝λ y (x,y)+jλ x (x,y) (7)
wherein lambda is r And (x, y) is the two-dimensional air gap relative flux guide of the permanent magnet linear motor.
Step three: calculating the normal air gap flux density and the tangential air gap flux density of the permanent magnet linear motor during slotting according to the improved two-dimensional air gap relative flux guiding function in the second step;
conjugate complex number lambda of slotless air gap flux density and improved two-dimensional air gap relative flux guide function r * The product of (x, y) is equal to the slotted air gap flux density, i.e.:
B s (x,y)＝B nos (x,y)·λ r * (x,y) (8)
wherein B is s (x, y) is the magnetic density with grooves, B nos (x, y) is the magnetic density without groove, lambda r * (x, y) is the complex conjugate of the two-dimensional air gap relative flux guide;
writing the slotted magnetic density and the ungrooved magnetic density into a complex form:
B s (x,y)＝B ys (x,y)+jB xs (x,y) (9)
B nos (x,y)＝B ynos (x,y)+jB xnos (x,y) (10)
wherein B is ys (x, y) is the normal magnetic density of the grooved magnetic density, B xs (x, y) is tangential magnetic flux density of grooved magnetic flux density, B ynos (x, y) is the normal magnetic density of the slotless magnetic density, B xnos (x, y) is tangential magnetic density of the slotless magnetic density;
calculating the normal air gap flux density and the tangential air gap flux density of the permanent magnet linear motor during slotting according to the improved two-dimensional air gap relative flux guiding function, the slotted flux density and the ungrooved flux density:
B ys (x,y)＝B ynos (x,y)·λ y (x,y)+B xnos (x,y)·λ x (x,y) (11)
B xs (x,y)＝B xnos (x,y)·λ y (x,y)-B ynos (x,y)·λ x (x,y) (12)
wherein B is ys (x, y) is a permanent magnet straight lineNormal air gap flux density when motor is grooved, B xs And (x, y) is tangential air gap flux density when the permanent magnet linear motor is grooved.
Step four: calculating the empty load flux density of an air gap area when the permanent magnet linear motor is grooved according to the air gap flux density of the first step and the improved two-dimensional air gap relative flux guiding function, calculating the flux linkage generated by a single-turn coil according to the empty load flux density, and calculating the empty load counter potential generated by a one-phase winding according to the flux linkage generated by the single-turn coil;
according to formulas (4) and (7), the empty magnetic density of an air gap area when the permanent magnet linear motor is grooved is obtained as follows:
B 3ys (x,y)＝B 3ynos (x,y)·λ y (x,y)+B 3xnos (x,y)·λ x (x,y) (13)
B 3xs (x,y)＝B 3xnos (x,y)·λ y (x,y)-B 3ynos (x,y)·λ x (x,y) (14)
wherein B is 3ys (x, y) represents the tangential slotted flux density of the air gap region, B 3xs (x, y) represents the magnetic flux density of the grooves normal to the air gap region;
to obtain the flux linkage generated by the single turn coil, the air gap of formula (4) is densified into fourier series form:
wherein B is yn (n) represents the magnitude of each subharmonic magnetic flux density of the normal ungrooved magnetic flux density, B xn (n) represents the tangential slotless magnetic flux density magnitude of each subharmonic of the magnetic flux density.
The magnetic linkage psi generated by the single-turn coil c The method comprises the following steps:
wherein L is a For the length of the iron core, a y ＝y 1 t s For coil pitch, y 1 Is the number of slots spanned by the coil.
The no-load counter potential induced by the single-turn coil is obtained as follows:
substituting formula (15) into formula (13) to obtain air gap flux density B 3ys (x, y) is:
substituting equation (18) into equation (16) yields the flux linkage ψ produced by a single turn coil c The method comprises the following steps:
no-load counter potential E generated by the one-phase winding φ The method comprises the following steps:
wherein N is 1 For each phase winding series turns, phase A theta 0 =0, b phase θ 0 =2pi/3, phase c θ 0 ＝4π/3，k dn In order to distribute the coefficients of the power distribution,for the slot opening coefficient, v 1 For the speed of the motor rotor, B yn (n) is the Fourier coefficient, B xn (n) is the Fourier coefficient, when y 1 Odd number of grooves, then a 0 ＝t s /2，cos(mza 0 ) Cos (mpi), when y 1 An even number of slots, then a 0 ＝0，cos(mza 0 )＝1。
The magnitude of the no-load counter potential is related to the harmonic amplitude of the flux density of the slotless air gap and the harmonic amplitude of the relative flux guide of the two-dimensional air gap. In general, for integer slots, the tangential magnetic density is small and B can be ignored xn (n)λ m (m) further reduced to consider normal onlyMagnetic density harmonic amplitude B yn (n) facilitating computation. For fractional slot, especially the matching of the polar slots with more polar numbers than the number of teeth, the tangential magnetic density is larger, B xn (n)λ m (m) is not negligible.
Step five: and (3) calculating the thrust of the permanent magnet linear motor according to the no-load counter potential in the step four, and verifying the correctness of the calculation method of the no-load counter potential and the thrust of the permanent magnet linear motor with the integer slot and fractional slot structure by using a finite element.
Obtaining the thrust F of the permanent magnet linear motor according to the no-load counter potential of the formula (20) x The method comprises the following steps:
wherein p is e Representing the electromagnetic power of the motor E a 、E b 、E c The no-load counter potential of the A, B, C phase is shown, a, B, C three-phase currents are respectively adopted, and I is a current effective value.
And verifying the correctness of the calculation method of the no-load back electromotive force and the thrust of the permanent magnet linear motor by using a finite element method. Examples two structures of the integer slot winding 18 slot 6 pole and the fractional slot winding 12 slot 14 pole were analyzed respectively, and parameters of motor structure are shown in table 1, wherein each motor adopts two slot type structures, namely a half-closed slot structure (b s ≤t s 2) and greater slot width (b) s ≥t s The rectangular slot configuration of/2) illustrates the effect of slot width on motor parameters.
Table 1 structural parameters of permanent magnet linear motor
(1) Improved two-dimensional air gap relative flux-guide calculation:
the integer groove 18 groove 6 poles and the fractional groove 12 groove 14 poles obtained according to (5) and (6) adopt a semi-closed groove structure and a rectangular groove structure, and are arranged at the center y of an air gap 0 ＝h m The improved two-dimensional air gap relative flux guide distribution at +delta/2 is shown in figures 3, 4, 5 and 6, the results of an analytic method and a finite element method can be better fitted, the improved two-dimensional air gap relative flux guide can be known to better reflect the influence of cogging on the normal and tangential distribution of a magnetic field, and the problem of difficult solution on the current tangential magnetic field is solved.
(2) No-load back emf and thrust calculations:
the operating frequencies of the permanent magnet linear motors with the integer slot 18, the slot 6 and the fractional slot 12 and the slot 14 are f=4Hz and f=10Hz respectively, and the no-load counter potential results obtained by the formula (20) are shown in figures 7, 8, 9 and 10. The effective value of the current fed to both motors is 5A, and the thrust calculation curves obtained by the formula (21) are shown in FIGS. 11, 12, 13 and 14. Wherein figures 13 and 14 show the thrust force comparison curves when the fractional slot 12 and the slot 14 have the same number of turns in series for each phase winding, and single and double layer windings are respectively adopted.
The back electromotive force and thrust results obtained by the analytic methods and the finite element method are basically consistent, and the analytic methods better reflect the change curves of the no-load back electromotive force and the thrust along with time. It can be seen that the result error of the integer slot and fractional slot semi-closed slot structure is smaller, and the result error of the fractional slot winding rectangular slot structure is larger. For a rectangular slot structure, the reason for error is that the influence of adjacent tooth slot effect is larger and larger along with the increase of the ratio of the width of a slot to the pitch, and the influence of adjacent tooth slot effect is ignored because the two-dimensional air gap relative flux guide is a single slot model, so that the tangential air gap relative flux guide error is larger, and the error can exist in counter potential and thrust.
In comparison of solving time, taking the fractional slot structure 12 and the 14-pole PMLSM as an example, the solving time is one electrical period, and the number of sampling points is 100. The analysis method can solve the improved two-dimensional air gap relative flux guide, air gap flux density, no-load counter potential and thrust parameters at one time, and when the maximum frequency of harmonic wave is 50, the calculation result is basically unchanged. The finite element method pretreatment modeling takes a lot of time, the cell subdivision length at the air gap is 0.5mm, and the total subdivision nodes of the model are 29253. The CPU is configured as i7-7700HQ,2.8GHz, the memory 32G, the simulation time consumption of the analytic method and the finite element method is 2.5s and 100s respectively. All the calculation in the analytic method is sum calculation, the electromagnetic parameters can be rapidly calculated, the solving efficiency is far higher than that of the finite element method, the solving precision of the finite element method is high, and the calculation time is increased along with the increase of the subdivision grids. The above results demonstrate the correctness of the calculation method employed by the present invention.
The foregoing description of the preferred embodiments of the invention is not intended to be limiting, but rather is intended to cover all modifications, equivalents, alternatives, and improvements that fall within the spirit and scope of the invention.
Claims (5)
1. The method for calculating the no-load counter potential and the thrust of the permanent magnet linear synchronous motor is characterized by comprising the following steps of:
step one: constructing an air gap field analysis model of the slotless permanent magnet linear motor, and obtaining the slotless magnetic flux density of an air gap region through a separation variable method and boundary conditions;
step two: taking a groove as an analysis model, selecting the center of the groove as an origin, constructing a normal two-dimensional air gap relative flux guiding function and a tangential two-dimensional air gap relative flux guiding function when the permanent magnet linear motor is grooved, and constructing an improved two-dimensional air gap relative flux guiding function of the permanent magnet linear motor by the normal two-dimensional air gap relative flux guiding function and the tangential two-dimensional air gap relative flux guiding function;
the relative flux guide function of the normal two-dimensional air gap when the permanent magnet linear motor is grooved is as follows:
the tangential two-dimensional air gap relative flux guide function when the permanent magnet linear motor is grooved is as follows:
wherein lambda is y (x, y) is the normal two-dimensional air gap relative flux guide, lambda x (x, y) is tangential two-dimensional air gap relative flux guide, a 0 For the distance of the slot centerline from the a-phase winding axis, z=2pi/t s ，t s Is tooth pitch, b s In order to be a groove width, beta (y) is a nonlinear function;
the improved two-dimensional air gap relative flux guide function of the permanent magnet linear motor is as follows:
λ r (x,y)＝λ y (x,y)+jλ x (x,y)
wherein lambda is r (x, y) is the two-dimensional air gap relative flux guide of the permanent magnet linear motor;
step three: calculating the normal air gap flux density and the tangential air gap flux density of the permanent magnet linear motor during slotting according to the improved two-dimensional air gap relative flux guiding function in the second step;
step four: calculating the empty load flux density of an air gap area when the permanent magnet linear motor is grooved according to the air gap flux density of the first step and the improved two-dimensional air gap relative flux guiding function, calculating the flux linkage generated by a single-turn coil according to the empty load flux density, and calculating the empty load counter potential generated by a one-phase winding according to the flux linkage generated by the single-turn coil;
the empty magnetic density of the air gap area when the permanent magnet linear motor is grooved is as follows:
B 3ys (x,y)＝B 3ynos (x,y)·λ y (x,y)+B 3xnos (x,y)·λ x (x,y)
B 3xs (x,y)＝B 3xnos (x,y)·λ y (x,y)-B 3ynos (x,y)·λ x (x,y)
wherein B is 3ys (x, y) represents the magnetic flux density of the grooves normal to the air gap region, B 3xs (x, y) represents the tangential slotted flux density of the air gap region; b (B) 3xnos (x, y) represents the air gap region tangential slotless magnetic fieldSecret B 3ynos (x, y) represents the normal ungrooved flux density of the air gap region;
the magnetic linkage psi generated by the single-turn coil c The method comprises the following steps:
wherein L is a For the length of the iron core, a y ＝y 1 t s For coil pitch, y 1 The number of slots spanned by the coil;
no-load counter potential E generated by one phase winding φ The method comprises the following steps:
wherein N is 1 For each phase winding series turns, phase A theta 0 =0, b phase θ 0 =2pi/3, phase c θ 0 ＝4π/3，k dn In order to distribute the coefficients of the power distribution,for slot opening coefficient, τ is pole pitch, k=pi/τ, v 1 For the speed of the motor rotor, B yn (n) is the Fourier coefficient, B xn (n) is the Fourier coefficient, when y 1 Odd number of grooves, then a 0 ＝t s /2，cos(mza 0 ) Cos (mpi), when y 1 An even number of slots, then a 0 ＝0，cos(mza 0 )＝1；
Step five: and (3) calculating the thrust of the permanent magnet linear motor according to the no-load counter potential in the step four, and verifying the correctness of the no-load counter potential and the thrust of the integer slot and the fractional slot permanent magnet linear motor by using a finite element.
2. The method for calculating the no-load back electromotive force and the thrust of the permanent magnet linear synchronous motor according to claim 1, wherein the air gap magnetic field analysis model of the slotless permanent magnet linear synchronous motor is as follows:
wherein A is z2 (x, y) is the vector magnetic potential of the permanent magnet region, A z3 (x, y) is the vector magnetic potential of the air gap region,k＝π/τ，M 0 ＝B r /μ 0 ，M 0 is the magnetic pole magnetization intensity, B r Mu, the residual magnetism of the magnetic pole 0 Is air permeability, a p ＝L m /τ，L m Is long in magnetic pole and τ is pole pitch.
3. The method for calculating the no-load back electromotive force and thrust force of a permanent magnet linear synchronous motor according to claim 2, wherein the boundary condition is:
wherein h is m Is of permanent magnet height, delta is the length of the air gap, B 2x Is the normal magnetic density of the magnetic pole area, B 3x Is the normal magnetic density of the air gap area, B 2y Is the tangential magnetic density of the magnetic pole area, B 3y Tangential magnetic density of the air gap area;
the air gap area slotless magnetic flux density obtained by the separation variable method and the boundary condition is as follows:
wherein B is 3xnos (x, y) represents the tangential slotless flux density of the air gap region, B 3ynos (x, y) represents the normal ungrooved flux density of the air gap region.
4. The method for calculating the no-load back electromotive force and the thrust force of the permanent magnet linear synchronous motor according to claim 1, wherein the method for calculating the normal air gap flux density and the tangential air gap flux density when the permanent magnet linear synchronous motor is grooved according to the improved two-dimensional air gap relative flux guiding function in the second step is as follows:
calculating the flux density of the slotted air gap:
B s (x,y)＝B nos (x,y)·λ r * (x,y)
wherein B is s (x, y) is the magnetic density with grooves, B nos (x, y) is the magnetic density without groove, lambda r * (x, y) is the complex conjugate of the two-dimensional air gap relative flux guide;
writing the slotted magnetic density and the ungrooved magnetic density into a complex form:
B s (x,y)＝B ys (x,y)+jB xs (x,y)
B nos (x,y)＝B ynos (x,y)+jB xnos (x,y)
wherein B is ys (x, y) is the normal magnetic density of the grooved magnetic density, B xs (x, y) is tangential magnetic flux density of grooved magnetic flux density, B ynos (x, y) is the normal magnetic density of the slotless magnetic density, B xnos (x, y) is tangential magnetic density of the slotless magnetic density;
calculating the normal air gap flux density and the tangential air gap flux density of the permanent magnet linear motor during slotting according to the improved two-dimensional air gap relative flux guiding function, the slotted flux density and the ungrooved flux density:
B ys (x,y)＝B ynos (x,y)·λ y (x,y)+B xnos (x,y)·λ x (x,y)
B xs (x,y)＝B xnos (x,y)·λ y (x,y)-B ynos (x,y)·λ x (x,y)
wherein B is ys (x, y) is the normal air gap flux density when the permanent magnet linear motor is grooved, B xs And (x, y) is tangential air gap flux density when the permanent magnet linear motor is grooved.
5. The method for calculating the no-load back electromotive force and thrust force of a permanent magnet linear synchronous motor according to claim 1, wherein the thrust force F of the permanent magnet linear synchronous motor x The method comprises the following steps:
wherein p is e Representing the electromagnetic power of the motor E a 、E b 、E c The no-load counter potential of the A, B, C phase is shown, a, B, C three-phase currents are respectively adopted, and I is a current effective value.
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Citations (10)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103605858A (en) * | 2013-11-27 | 2014-02-26 | 华中科技大学 | Steady-state characteristic analysis method for linear induction motor |
| EP2768117A1 (en) * | 2013-02-18 | 2014-08-20 | Siemens Aktiengesellschaft | Rotor of a reluctance machine |
| CN105005692A (en) * | 2015-07-08 | 2015-10-28 | 三峡大学 | Analytical method based permanent magnet motor field analysis and torque calculation method |
| CN105787158A (en) * | 2016-02-05 | 2016-07-20 | 天津大学 | Permanent magnet synchronous linear motor modeling and characteristic analyzing method based on equivalent magnetic circuit method |
| CN107612256A (en) * | 2017-05-25 | 2018-01-19 | 合肥硬核派科技有限公司 | A kind of Optimization Design of magnetic pole sectional type durface mounted permanent magnet synchronous motor |
| CN108021039A (en) * | 2017-12-23 | 2018-05-11 | 西安交通大学 | A kind of Linear motor feeding system electromechanics integrated modelling approach |
| CN109672304A (en) * | 2018-12-18 | 2019-04-23 | 安徽大学 | A kind of moving-magnetic type permanent magnetic linear synchronous motor design method inhibited based on longitudinal end effect |
| CN110690770A (en) * | 2019-11-04 | 2020-01-14 | 郑州轻工业学院 | Method for solving complex air gap relative magnetic conductance and magnetic field of stator slotted permanent magnet motor |
| CN110890827A (en) * | 2019-12-20 | 2020-03-17 | 郑州轻工业大学 | Improved method for solving complex air gap relative magnetic conductance and magnetic field of permanent magnet linear motor |
| CN111651914A (en) * | 2020-05-14 | 2020-09-11 | 福州大学 | Magnetic field analytic calculation method of bearingless flux switching motor |
-
2020
- 2020-10-28 CN CN202011171011.8A patent/CN112329293B/en active Active
Patent Citations (10)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| EP2768117A1 (en) * | 2013-02-18 | 2014-08-20 | Siemens Aktiengesellschaft | Rotor of a reluctance machine |
| CN103605858A (en) * | 2013-11-27 | 2014-02-26 | 华中科技大学 | Steady-state characteristic analysis method for linear induction motor |
| CN105005692A (en) * | 2015-07-08 | 2015-10-28 | 三峡大学 | Analytical method based permanent magnet motor field analysis and torque calculation method |
| CN105787158A (en) * | 2016-02-05 | 2016-07-20 | 天津大学 | Permanent magnet synchronous linear motor modeling and characteristic analyzing method based on equivalent magnetic circuit method |
| CN107612256A (en) * | 2017-05-25 | 2018-01-19 | 合肥硬核派科技有限公司 | A kind of Optimization Design of magnetic pole sectional type durface mounted permanent magnet synchronous motor |
| CN108021039A (en) * | 2017-12-23 | 2018-05-11 | 西安交通大学 | A kind of Linear motor feeding system electromechanics integrated modelling approach |
| CN109672304A (en) * | 2018-12-18 | 2019-04-23 | 安徽大学 | A kind of moving-magnetic type permanent magnetic linear synchronous motor design method inhibited based on longitudinal end effect |
| CN110690770A (en) * | 2019-11-04 | 2020-01-14 | 郑州轻工业学院 | Method for solving complex air gap relative magnetic conductance and magnetic field of stator slotted permanent magnet motor |
| CN110890827A (en) * | 2019-12-20 | 2020-03-17 | 郑州轻工业大学 | Improved method for solving complex air gap relative magnetic conductance and magnetic field of permanent magnet linear motor |
| CN111651914A (en) * | 2020-05-14 | 2020-09-11 | 福州大学 | Magnetic field analytic calculation method of bearingless flux switching motor |
Non-Patent Citations (2)
| Title |
|---|
| 新型磁场调制式永磁直线同步电机的特性研究;王明杰;《中国优秀博士学位论文全文数据库》(第2期);C042-27 * |
| 永磁直线同步电机空载反电动势和推力的解析计算;王明杰等;《电工技术学报》;第36卷(第5期);954-963 * |
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