A method for restraining positioning force of a permanent magnet linear synchronous motor

Abstract

The application discloses a permanent magnet linear synchronous motor positioning force suppression method, and particularly relates to the following steps: weakening the end longitudinal magnetic flux by externally chamfering the two end portions of a stator, changing the amplitude and phase of the end force by changing the length of the stator core of the motor, and adjusting the cogging force by internally chamfering the top of the internal tooth, wherein the relationship among the width, height of the external and internal chamfering and the length of the stator core of the stator satisfies the following requirements: the resultant amplitude of the end force and the cogging force of the stator module is the same but the phases are opposite. The method is simple and easy to implement, and provides a new idea for the positioning force suppression method of the permanent magnet synchronous linear motor adopting double-layer fractional slot concentrated winding.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of permanent magnet linear synchronous motors, and particularly relates to a permanent magnet linear synchronous motor positioning force suppression method. BACKGROUND

[0002] Compared with a rotary motor, a linear motor does not need to use a mechanical device such as a ball screw to convert motion, and therefore does not need to consider the influence of reverse clearance, return difference and elastic deformation of the mechanical device, has the advantages of high control precision, low noise, high transmission efficiency and long service life, and has a wide application in the fields of precision machining equipment, lithography machines, logistics transportation and cordless elevators. Among them, the permanent magnet synchronous linear motor has a wide application market due to its advantages of high thrust density, high efficiency and simple excitation mode, and is the most used type in commercial applications.

[0003] However, the thrust fluctuation of the permanent magnet synchronous linear motor is too large to limit the motion control of the motor and its use in the precision machining field. At present, the thrust fluctuation of the permanent magnet linear synchronous motor mainly comes from the cogging force, end effect force, ripple thrust, friction force and load disturbance. Among them, the positioning force composed of the cogging force and the end force is the main factor causing the thrust fluctuation. The cogging force is a static magnetic resistance force that fluctuates with the position of the primary due to the uneven distribution of the air gap magnetic field caused by the slotting of the primary core; the end force is a large static magnetic resistance force formed between the primary end core and the secondary magnetic pole due to the longitudinal break of the primary core of the linear motor.

[0004] The existing methods for suppressing the end force mainly include adjusting the length of the stator core, using auxiliary teeth and changing the shape of the motor edge. Adjusting the length of the stator core is the simplest and most convenient method, but it cannot eliminate the high-order harmonics in the end force; using auxiliary teeth and optimizing the shape of the motor edge can eliminate the positioning force, but it increases the processing difficulty. There are many methods for suppressing the cogging force, including optimizing the pole arc coefficient, opening auxiliary slots at the top of the teeth, slanting the slots and slanting the poles, which mostly refer to the methods for suppressing the cogging torque of the rotary motor. Overall, the existing positioning force suppression methods mostly optimize the end force and the cogging force independently, and do not deeply explore the coupling relationship between the cogging force and the end force. SUMMARY

[0005] The application aims to solve the problems existing in the prior art, and provides a permanent magnet linear synchronous motor positioning force suppression method.

[0006] Technical Solution: The present invention provides a method for suppressing the positioning force of a permanent magnet linear synchronous motor. Specifically, the method comprises: performing external chamfering on both ends of the stator to weaken the longitudinal magnetic flux at the ends, and changing the amplitude and phase of the end force by changing the length of the motor stator core; and performing internal chamfering on the internal tooth tops to adjust the cogging force. The relationship between the width and height of the external and internal chamfers and the stator core length meets the following requirements:

[0007] The resultant force of the end force and the cogging force of the stator module has the same amplitude and opposite phase.

[0008] Furthermore, the external chamfer includes a left-end external chamfer and a right-end external chamfer, and the left-end external chamfer and the right-end external chamfer are distributed on the outside of the stator end teeth; the internal chamfer is distributed on both sides of the stator internal teeth and the inside of the end teeth; the length of the motor stator core is the horizontal distance from the left end face to the right end face of the stator.

[0009] Furthermore, the width of the stator external chamfer is recorded as W o , the height is recorded as h o , the width of the internal tooth chamfer is recorded as W i , the height is recorded as h i , the length of the motor stator core is recorded as L p ;W o , h o , W i , h i , and L p , combined into variable x, construct the following objective function:

[0010] minf(x)=(f detpk2 (x),f eavg (x))

[0011] x=(L p ,w i ,h i ,w o ,h o )

[0012] Among them, f detpk2 (.) represents the peak value of the motor positioning force, f eavg (.) represents the average electromagnetic thrust of the motor.

[0013] Furthermore, the variable W is determined by the following method: o and h o Constraints:

[0014] Step 4.1: Calculate different W o and h o Under the combination of endpk2 and end force fend :

[0015]

[0016] wherein, δ is the equivalent air gap length, φ m is the maximum value of the end longitudinal magnetic flux, μ0 is the vacuum permeability, k1 is the flux compression coefficient, τ is the pole pitch, l ef is the stator core lamination length, x1 is the displacement of the motor in the x-axis movement direction, ΔW is the magnetic field magnetic energy change amount, and the expression of ΔW is as follows:

[0017]

[0018] wherein, n is the Fourier expansion number;

[0019] Step 4.2: Draw the end force amplitude curve of the motor under the combination of different W o and h o , select the curve whose amplitude change range exceeds the preset value to determine the range of variables h o and w o .

[0020] Further, the range of h o is 1-3mm, and the range of w o is 2-6mm.

[0021] Further, the following method is used to determine the constraint condition of variable L p :

[0022] Step 5.1: Calculate the end force f p of the stator on both sides under different L end :

[0023] f end = f endL + f endR

[0024] wherein, f endL , f endR are the end forces on the left and right sides of the stator, and the expressions of f endL , f endR are as follows:

[0025]

[0026] wherein, F0 is the end force DC component, F0 is the end force DC component, n is the Fourier expansion number; F sn , F cn are the amplitudes of the nth harmonic of the sine and cosine components, respectively, and Δ = L p-kτ, k is any positive integer, τ is pole pitch, x1 is the displacement of motor in x-axis direction;

[0027] Step 5.2: draw the amplitude curve of end force f on both sides of the stator under different L p end , and determine the optimization range of L P .

[0028] Further, the optimization range of L P is 65-70mm

[0029] Further, the constraint conditions of variables W i and h i are determined as follows:

[0030] Step 6.1: calculate the motor cogging force f i under different combinations of W i and h cog :

[0031]

[0032] wherein, α is the offset distance of tooth center from the center of permanent magnet, V is the air gap volume, μ0 is the vacuum permeability, B is the air gap flux density of motor on the armature surface, and the expression is as follows:

[0033]

[0034] wherein, B r (θ) is the residual magnetism of permanent magnet, h m (θ) is the magnetization direction length of permanent magnet, δ(θ, α) is the effective air gap length of motor, and θ is the angle in the secondary motion direction of motor;

[0035] By changing W i and h i , adjusting δ(θ, α), the cogging force is changed;

[0036] Step 6.1: draw the amplitude curve of motor cogging force under different combinations of w i and h i , so as to determine the optimization range of W1 and the optimization range of h1.

[0037] Further, the optimization range of w i is 0.8-2mm, and the optimization range of h i is 0.2-2mm.

[0038] Further, the genetic algorithm is used to solve the objective function.

[0039] ​Beneficial effects: the application can effectively reduce the motor positioning force by the inner-outer unequal chamfer and the stator core length adjustment, while the slot fill factor of the stator is not changed, the processing is easy, and the application provides a new idea for the positioning force suppression method of the permanent magnet synchronous linear motor adopting the double-layer fractional slot concentrated winding, and the method is simple and easy to realize. BRIEF DESCRIPTION OF DRAWINGS

[0040] Figure 1 is the positioning force suppression method model schematic diagram in the application example.

[0041] Figure 2 is the end force amplitude scanning diagram under different end chamfer sizes in the application example.

[0042] Figure 3 is the end force amplitude scanning diagram under different stator core lengths in the application example.

[0043] Figure 4 is the tooth slot force amplitude scanning diagram under different tooth chamfers in the application example.

[0044] Figure 5 is the optimization result diagram obtained by using the genetic algorithm optimization in the application example.

[0045] Figure 6 is the robustness judgment diagram of the optimization result in the application example.

[0046] Figure 7 is the positioning force waveform comparison diagram before and after optimization in the application example.

[0047] Figure 8 is the Fourier analysis diagram of the final optimization result in the application example. DETAILED DESCRIPTION

[0048] The drawings that form a part of the present application are used to provide further understanding of the present application, the illustrative embodiments of the present application and the description thereof are used to explain the present application, and do not constitute improper limitation on the present application.

[0049] The permanent magnet synchronous linear motor positioning force suppression method based on inner-outer unequal chamfer provided by the application example is referred to Figure 1 , for the flat plate type permanent magnet synchronous linear motor, the adjustment on the stator module shape is performed by the external chamfer on the two ends of the stator and the change of the stator core length, the effective suppression of the end force is realized, the internal chamfer is performed at the internal tooth top to adjust the tooth slot force, finally, the stator chamfer parameters and the primary length (namely the core length) are used as the optimization variables to optimize the motor positioning force by using the genetic algorithm.

[0050] The external chamfers are respectively left end chamfer and right end chamfer, and the left end chamfer and the right end chamfer are distributed on both sides of the stator module along the z-axis of the set three-dimensional coordinate system; the internal tooth chamfer is distributed on both sides and the inner side of the end tooth of the internal tooth along the z-axis of the set coordinate system; the stator core length is the horizontal distance of the stator left end face to the right end face along the x-axis direction of the set three-dimensional coordinate system, and the mover module moves along the x-axis direction of the set three-dimensional coordinate system.

[0051] The relationship between the width, height of the stator module end external tooth chamfer and internal tooth chamfer and the stator core length at least meets the following requirements, that is, the end force and the slot force of the stator module have the same amplitude but opposite phases.

[0052] The end force of the motor to be optimized under different end chamfer sizes is scanned, and the initial range of the optimization variable is determined according to the scanning result, specifically:

[0053] Since the magnetic flux passing through the longitudinal end of the motor will also return to the magnetic pole below the mover under the principle of the shortest magnetic circuit, the change of the magnetic flux of the longitudinal edge of the mover causes the change of the energy storage of the air gap between the movers. The Fourier relationship of the air gap magnetic field energy storage is:

[0054]

[0055] In the formula, δ is the equivalent air gap length, k1 is the magnetic flux compression coefficient, τ is the pole pitch, l ef is the stator core stacking length, φ m is the maximum value of the longitudinal magnetic flux of the end, μ0 is the vacuum permeability; ΔW is the magnetic energy change, n is the Fourier expansion number, x1 is the displacement of the motor in the x-axis movement direction;

[0056] According to the virtual displacement method, the motor end force is:

[0057]

[0058] The end force peak value is:

[0059]

[0060] The end force peak value is greatly affected by the magnetic flux, and the maximum value of the longitudinal magnetic flux of the motor after the external chamfer is weakened, so as to realize the weakening of the end force of the motor;

[0061] The end force of the motor to be optimized under different end chamfer sizes is scanned, and the initial range of the optimization variable is obtained according to the scanning result in the embodiment; the same chamfer width and height are used for the external chamfers of the left and right ends of the motor, the chamfer direction is along the z-axis direction of the reference coordinate axis, and the chamfer size is scanned by parameterization using Ansys Maxwell;

[0062] Figure 2 The end force amplitude curve of the permanent magnet synchronous linear motor under different end chamfer sizes, the variable h is selected from the curve with large amplitude variation range o and w o The optimization range is 1-3mm, 2-6mm.

[0063] The length of the stator core is changed to adjust the amplitude and phase of the end force, and the relationship between the left and right end forces of the motor is expressed as follows:

[0064]

[0065] In the formula, f endL , f endR are the left and right end forces respectively, F0 is the direct current component of the end force, F sn , F cn are the amplitudes of the nth harmonic of the sine and cosine components respectively, Δ = L p -kτ, where L P is the length of the motor stator core, τ is the pole pitch, and k is any positive integer.

[0066] Without considering the pulsating force, the resultant end force is:

[0067]

[0068] By optimizing the length of the motor primary core L P , the phase difference between the left and right end forces is adjusted, the amplitude and phase of the end force f end are changed;

[0069] Figure 3 The end force amplitude of the permanent magnet synchronous linear motor under different stator core lengths is selected from the variable L P The optimization range is 65-70mm.

[0070] The internal tooth chamfer changes the maximum longitudinal magnetic flux by adjusting the chamfer width w i and the chamfer height h i to weaken the cogging force;

[0071] According to the virtual displacement method, the formula for calculating the motor cogging force f cog is:

[0072]

[0073] In the formula, α is the offset distance of the tooth center from the center of the permanent magnet, and B is the distribution of the air gap flux density of the motor on the armature surface;

[0074] The distribution of the air gap flux density of the motor on the armature surface is:

[0075]

[0076] B r (θ) is the residual magnetization of the permanent magnet, h m (θ) is the magnetization direction length of the permanent magnet, δ(θ,α) is the effective air gap length of the motor, θ is the angle in the motor secondary motion direction;

[0077] The air gap magnetic flux density is related to the residual magnetization and the magnetization direction length and the effective air gap length δ(θ,α), but the residual magnetization and the magnetization direction length are selected values according to the permanent magnet material and the slot fill rate and other factors in the preliminary design, and it is not appropriate to make changes, so it is necessary to adjust the effective air gap length δ(θ,α), and the δ(θ,α) can be quickly adjusted by chamfering. After chamfering, the air gap height increases and the effective air gap length decreases, so as to realize the weakening of the amplitude of the cogging force.

[0078] The cogging force of the motor to be optimized under different internal tooth chamfer sizes is scanned, and the initial range of the optimization variable is determined according to the scanning result; in this embodiment, the same chamfer width and height are used for the inner side of the motor side tooth and the internal tooth, the chamfer direction is along the reference coordinate axis z axis direction, and Ansys Maxwell is used for parameterized scanning of the chamfer size.

[0079] Figure 4 The amplitude of the cogging force of the permanent magnet synchronous linear motor under different internal tooth chamfer sizes is selected, the curve with large amplitude change range is determined as the variable w i ,h i The optimization range is 0.8-2mm, 0.2-2mm.

[0080] An optimization function is established for the motor to be optimized:

[0081] minf(x)=(f detpk2 (x),f eavg (x))

[0082] x=(L p ,w i ,h i ,w o ,h o )

[0083] In the formula, f detpk2 (.) represents the peak-to-peak value of the motor positioning force, f eavg (.) represents the average value of the motor electromagnetic thrust, x=(L P ,w i ,h i ,w o ,h o ) represents the group of variables to be optimized, L P ,w i ,h i ,w o ,ho They represent the stator core length, inner chamfer width, inner chamfer height, outer chamfer width, and outer chamfer height respectively.

[0084] The genetic algorithm is used to combine the objective function and the set of variables to be optimized to obtain the optimal result, including the following steps:

[0085] Step S1: Set the optimization target, the optimization target is the peak-to-peak value of the motor positioning force f detpk2 Minimum and motor electromagnetic thrust f eavg The average value is the largest;

[0086] Step S2: Setting the motor parameter optimization range of the linear motor according to the parametric scanning result, wherein the motor parameters include the stator core length L in the stator module. P , Internal tooth chamfer width w i , Internal tooth chamfer height h i , External chamfer width w o and the external chamfer height h o ;

[0087] Step S3: Set the genetic algorithm parameters, including the number of populations, the maximum and minimum evolutionary generations, the selection method and number of maternal lines, the crossover point and crossover method, the mutation point and mutation method, etc. After setting the optimization parameters, perform iterative optimization to finally obtain the Pareto optimal solution.

[0088] Steps S1, S2, and S3 are implemented using joint simulation of Ansys Maxwell, Workbench, and optislang, and are optimized by calling the built-in genetic algorithm of optislang.

[0089] Figure 5 This is a graph of the optimization results obtained by using the genetic algorithm in the example of the present invention. In the figure, the vertical axis represents the average electromagnetic thrust of the motor, the horizontal axis represents the peak-to-peak value of the motor positioning force, and the Pareto front represents the motor optimization Pareto solution set. Considering that the minimum positioning force and the maximum electromagnetic thrust have the same weight value, the point in the middle section of the Pareto solution set is selected as the optimization result, and the corresponding peak-to-peak value of the positioning force and the average thrust are 1.72N and 59.71N, respectively.

[0090] Robust analysis: The performance of the optimization solution will be affected by the machining accuracy, and its performance changes within the machining error range are calculated.

[0091] Figure 6For the optimized robust analysis diagram of the motor, the machining precision requirement is 0.05 mm, and the parameters are increased and decreased by 0.05 mm based on the parameter basis, which are error scheme 1 and error scheme 2, respectively. The thrust curve in the figure is obtained by simulation using Ansys Maxwell within one electrical period of 12 ms. It can be found that the thrust curves of the error scheme and the optimization scheme are approximately consistent.

[0092] Figure 7 For the comparison diagram of the positioning force waveform before and after optimization, it can be found that the amplitude of the positioning force after optimization is reduced to 0.86 N from the original 6.81 N, which is reduced by 87.35%, and the positioning force of the linear motor is greatly weakened.

[0093] Figure 8 For the Fourier analysis diagram of the optimized cogging force, end force and positioning force, it can be found that the fundamental wave amplitude of the cogging force and the fundamental wave amplitude of the end force cancel each other out, so that the fundamental wave amplitude of the positioning force is weakened, and the remaining harmonics are also inhibited to different degrees.

[0094] In addition, it should be noted that each specific technical feature described in the above specific embodiments can be combined in any appropriate manner without contradiction. In order to avoid unnecessary repetition, various possible combinations are not described again in the present application.

Claims

1. A method for suppressing the positioning force of a permanent magnet linear synchronous motor, characterized in that: Specifically, the longitudinal magnetic flux at the ends of the stator is weakened by external chamfering, and the amplitude and phase of the end force are changed by changing the length of the motor stator core. Internal chamfering is also performed at the internal tooth top to adjust the cogging force. The relationship between the width and height of the external and internal chamfers and the stator core length meets the following requirements: The end force and the cogging force of the stator module have the same amplitude and opposite phase; The external chamfers include a left external chamfer and a right external chamfer, and the left external chamfer and the right external chamfer are distributed on the outside of the stator end teeth; the internal chamfers are distributed on both sides of the stator internal teeth and the inside of the end teeth; the length of the motor stator core is the horizontal distance from the left end face to the right end face of the stator; The width of the stator external chamfer is recorded as W o , the height is recorded as h o , the width of the internal tooth chamfer is recorded as W i , the height is recorded as h i , the length of the motor stator core is recorded as L p ;W o , h o , W i , h i , and L p , combined into variable x, construct the following objective function: minf(x)=(f detpk2 (x),f eavg (x)) x=(L p ,w i ,h i ,w o ,h o ) Among them, f detpk2 (.) represents the peak value of the motor positioning force, f eavg (.) represents the average electromagnetic thrust of the motor; The variable W is determined as follows: o and h o Constraints: Step a: Calculate different W o and h o Under the combination of endpk2 and end force f end : Where δ is the equivalent air gap length, φ m is the maximum longitudinal magnetic flux at the end, μ0 is the vacuum permeability, k1 is the magnetic flux compression coefficient, τ is the pole pitch, l ef is the stacked length of the stator core, x1 is the displacement of the motor in the x-axis direction, and ΔW is the change in magnetic energy of the magnetic field. The expression of ΔW is as follows: Where n is the number of Fourier expansions; Step b: Draw the motor at different W o and h o The end force amplitude curve under the combination of , select the curve whose amplitude variation range exceeds the preset value to determine the variable h o and w o scope; The variable L is determined by the following method: p Constraints: Step A: Calculate different L p The resultant force f on both sides of the stator under end : f end =f endL +f endR Among them, f endL 、f endR are the end forces on the left and right sides of the stator, f endL 、f endR The expression is as follows: Where F0 is the DC component of the end force, F0 is the DC component of the end force, n is the number of Fourier expansions; F sn 、F cn are the amplitudes of the nth harmonics of the sine and cosine components, respectively, Δ=L p -kτ, k is any positive integer, τ is the pole pitch, and x1 is the displacement of the motor in the x-axis direction; Step B: Draw different L p The resultant force f on both sides of the stator under end The amplitude curve is determined by the amplitude variation range L P Optimization scope; The variable W is determined as follows: i and h i Constraints: Calculate different W i and h i Calculate the motor cogging force f under the combination of cog : Where α is the offset distance between the tooth center and the permanent magnet center, V is the air gap volume, μ0 is the vacuum permeability, and B is the distribution of the motor's air gap flux density on the armature surface. The expression is as follows: Among them, B r (θ) is the remanence of the permanent magnet, h m (θ) is the length of the permanent magnet in the magnetizing direction, δ(θ,α) is the effective air gap length of the motor, and θ is the angle in the secondary motion direction of the motor. By changing W i and h i , adjust δ(θ,α) to change the cogging force; Draw different w i and h i Under the combination, the motor cogging force amplitude curve is obtained to determine the optimization range of W1 and the optimization range of h1.

2. A method for suppressing the positioning force of a permanent magnet linear synchronous motor according to claim 1, characterized in that: h o The range is 1-3mm, w o The range is 2-6mm.

3. The method for suppressing the positioning force of a permanent magnet linear synchronous motor according to claim 1, wherein: L P The optimization range is 65-70mm.

4. The method for suppressing the positioning force of a permanent magnet linear synchronous motor according to claim 1, wherein: w i The optimization range is 0.8-2mm, h i The optimization range is 0.2-2mm.

5. The method for suppressing the positioning force of a permanent magnet linear synchronous motor according to claim 1, characterized in that: Genetic algorithm is used to solve the objective function.

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