Magnetic Field Analysis and Magnetic Resistance Optimization of Moving Magnet Primary Segmented Permanent Magnet Synchronous Linear Motor

Abstract

In this paper, the moving-magnet segmented primary permanent magnet synchronous linear motor (SPPMSLM) with two primary stator units and one rotor is studied, the characteristics of magnetic field and force acting on the rotor during switching between two stator elements are analyzed. Firstly, the analytical expressions of the no-load air-gap magnetic field of SPPMSLM are derived by using the analytical method, and the results are verified by the finite element method, secondly, because the primary discontinuity in the structure of SPPMSLM results in the excessive magnetic resistance between the segments of the rotor, the size of the motor is simulated by the parameterized finite element method, the topology of adding auxiliary poles at both ends of the stator back iron is proposed, which is matched with the auxiliary teeth at the end of the primary stator unit, the effectiveness of the proposed structure in magnetic resistance reduction is evaluated by energy conversion method, which can provide some reference value for structure design and performance optimization of SPPMSLM.

1 Introduction

In recent years, permanent magnet synchronous linear motor (PMLSM) has been widely concerned by related application industries because of its advantages such as light weight, small volume, simple structure, no intermediate drive device, high thrust density and fast response speed. PMLSM is usually run on the stator covered with permanent magnet steel by the actuator of the primary winding with iron core. The winding of the actuator needs to be powered by the trailing wire, which limits the movable range of the actuator. In addition, a large amount of magnetic steel is needed to meet the needs of the long stroke operation, and the cost is huge. In order to meet the needs of long and smooth operation of factory production lines or logistics lines, literature [1] proposed a moving magnetic primary segmented permanent magnet linear motor model. Literature [2,3,4] established the motor simulation model based on the application of the moving magnetic segmented primary synchronous linear motor in the vertical direction lifting system, carried out the finite element analysis of the electromagnetic characteristics of the motor model and proposed the corresponding analytical calculation formula. Based on the mutual verification of finite element method and analytical method, literature [5] put forward the design criteria and calculation formula for each size of the body structure of the moving magnetic segmented primary synchronous linear motor. In literature [6, 7], the finite element method was used to study both the magnetic resistance and the tooth groove force of the segmented primary synchronous linear motor, and the proposed theory was verified by experiments. Literature [8] proposed the analytical formula of air gap magnetic density of fractional slot permanent magnet linear motor. However, the derivation of the analytical formula of the air gap magnetic density of the moving magnetic piecewise linear motor model under no-load is not mature in the existing papers. This paper uses the finite element method to study the air gap magnetic density waveform of the primary piecewise model and deduces the calculation formula, and verifies the accuracy of the analytical formula of the air gap magnetic density of this model by comparing the results of the analytical method with the finite element method.

Because of the primary structure of the discontinuous segment, the end force of the moving magnetic resistance when the stator element is moving in and out is much greater than the tooth groove force when the stator is coupling. Therefore, noise and vibration will be generated when the moving stator is passing through the segment, which will affect the stability in operation. How to weaken the end force caused by the motor moving between segments is a particularly important point to improve the motor performance. In literature [9], Halbach array arrangement of permanent magnet was adopted, and the positioning force was modulated by the magnetic accumulation effect of the arranged array, thus reducing thrust fluctuation. In literature [10], it was proposed to change the length of the teeth at the primary two sides of the end and use the side end effect to modulate each other so as to effectively weaken the thrust fluctuation. Literature [11] proposed a method to weaken the end force by changing the height of several side teeth at both ends of the primary stator element. Literature [12] proposed the method of changing the width of several side teeth at the end of the stator element to weaken the end force. Literature [11] proposed a way to divide the magnetic poles of permanent magnets to reduce the end force received during operation. The method used in literature [11,12,13] is mainly to optimize the structural size of the original model so as to weaken the end force on which the actuator runs in and out of the primary element. Literature [14] proposes a way of adding stepped auxiliary stages at both ends of the primary stator element to weaken the end force by adjusting the structural size of the auxiliary stages. Literature [15] further reduces the influence of the end force by combining the slanting pole arrangement of permanent magnets with the step type auxiliary teeth of the primary stator element. Literature [16] proposes a modified circular auxiliary stage placed on the end of the primary stator, which also has a very effective weakening effect on the end force of the secondary actuator running between segments. Literature [17] proposed a very advanced optimization method for thrust characteristics of flat permanent magnet linear motor. Literature [18, 19] proposed a new permanent magnet shape optimization method, which weakened the harmonic frequency of breath by modifying motor parameters to achieve performance optimization. The existing optimal design schemes all add auxiliary structure to the primary iron core. Since the motor under study is a moving magnetic setting, auxiliary poles can be added to both ends of the moving magnetic backplane to optimize the electromagnetic characteristics of the motor and weaken the positioning force by changing the structure of the magnetic backplane. In order to find an effective way to reduce the magnetic resistance, this paper proposed a method of adding auxiliary stages to both ends of the actuator back iron to weaken the end force received during operation between segments. Several auxiliary stage structures were designed and compared by finite element method, and then evaluated by energy conversion method to verify the effectiveness of reducing the magnetic resistance.

2 The Model of Discontinuous Sectional Primary Linear Motor

The SPPMLSM model studied in this paper is shown in Fig. 1. The stator of the linear motor is composed of primary units with windings, which are placed at certain intervals. The moving part consists of the secondary permanent magnet. The moving part starts to run after the primary winding is energized. The effective length of the stator element is L1, the spacing distance of the stator element is L2, and the effective distance of the actuator part is L. The effective distance of the actuator in the model is the sum of the effective length of the stator element and the length of the interval (L = L1 + L2). Such arrangement makes the total area of effective coupling between the moving part of the motor and the stator part constant in the process of moving, so that the three-phase current through each section of the stator element needs to be the same phase sequence and direction of each phase. When entering the next stator, the actuator is partially counteracted by the end force of the entering end in the same direction as the moving direction and the end force of the leaving exit end in the opposite direction, which makes the actuator run more stable.

Fig. 1

Finite element model of moving magnetic segmented primary permanent magnet synchronous linear motor

The moving magnetic segmented primary permanent linear motor has a moving length of 336 mm. It adopts a polar permanent magnet with the brand name NdFe42H16. The length of the permanent magnet is 18 mm, the width is 5 mm, the pole spacing is 21 mm, and the length of the primary stator element is 168 mm. The winding method adopted in this study is concentrated winding, with 200 turns per phase, 6 slots, slot spacing of 28 mm, and air gap between armature and starter of 2.5 mm. The specification of this motor model is shown in Table 1.

Table 1 The model parameters of the moving magnetic SPPMLSM

3 The Analysis of Air Gap Magnetic Field of Discontinuous Segmented Linear Motor

3.1 Analytical Formula of Air Gap Magnetic Density for Motor Model

The motor model with 4 poles and 3 slots studied in this paper belongs to fractional slot centralized winding. Because the repetition period of the magnet motive force waveform generated by the fractional slot winding group is not based on the distance between the poles, but on the distance between the unit motor, the number of slots occupied by each pole is different in a cycle. For this model, the number q per phase slot per pole is as follows:

$$ {\text{q}} = \frac{Z}{{2{\text{pm}}}} = \frac{{\text{k}}}{{\text{j}}} $$

(1)

where: Z is the number of slots; p is the polar logarithm; m is the phase number; k and j are the numerator and denominator of the simplified fraction. The simplified denominator j is even, so the polar logarithm of the unit motor takes the same value as j.

The analytical expression of no-load airgap magnetic field of primary segment linear motor with moving magnetic is derived, that is, the analytical expression of magnetic density waveform of permanent magnet is studied when the moving stator is coupled and the primary stator is not slotted. When the stator is not slotted, the air gap is evenly distributed, so the permeability per unit area in the air gap is:

$$ \Lambda = \frac{{\mu_{0} }}{\delta } $$

(2)

_{That is:}

$$ \delta = {\text{h}}_{{\text{m}}} + \delta_{0} $$

(3)

µ₀ is air permeability; δ is the sum of magnetization direction length h_m of permanent magnet and air gap length δ0 when the stator is not slotted.

Take the unit motor with stator coupling as an example. Because the air gap magnetic field under each pole is different, the air gap magnetic field under a pair of magnetic poles cannot be deduced separately. Think of the entire magnetic pole as a whole. Figure 2 shows the air gap magnetic density distribution when the pole number is 4, and the origin of coordinates is selected as the center point of the moving pole arrangement in the case of moving stator coupling.

Fig. 2

Magnetic density distribution of stator air gap without grooving

Within the interval of $x \in [ - 4\tau ,4\tau ]$, the air gap magnetic density can be expressed as follows:

$$ B_{\delta } (x) = \left\{ {\begin{array}{*{20}c} { - B_{\delta } ,2k\tau + (\frac{3 - \alpha }{2})\tau \le x \le 2k\tau + (\frac{3 + \alpha }{2})\tau } \\ \begin{gathered} \hfill \\ B_{\delta } ,2k\tau + (\frac{1 - \alpha }{2})\tau \le x \le 2k\tau + (\frac{1 + \alpha }{2})\tau \hfill \\ \end{gathered} \\ \begin{gathered} \hfill \\ 0,x \in {\text{other position}} \hfill \\ \end{gathered} \\ \end{array} } \right. $$

(4)

Among them, in the type $\tau$: is pole distance; $\alpha$ is the polar arc coefficient; k = 0, ±1, ±2.

B_δ is the amplitude of magnetic density of square wave air gap generated by permanent magnet:

$$ B_{\delta } = \frac{{B_{{\text{r}}} {\text{h}}_{m} }}{\delta } $$

(5)

where: B_r is the permanent magnetic strength of permanent magnet.

Since the magnetic density of the air gap is periodic, the Fourier transform can be applied to it. In the case that the stator is not grooved, the expression of the magnetic density of the air gap generated by the permanent magnet is:

$$ B_{\delta } (x) = \frac{{2B_{\delta } }}{\pi }\{ \sum\limits_{n = 1}^{\infty } {[\cos (\frac{n\pi (1 - \alpha )}{2}) - \cos (\frac{n\pi (1 + \alpha )}{2})]} \frac{{\sin (\frac{n\pi x}{\tau })}}{n}\} $$

(6)

Among them $x \in [ - 4\tau ,4\tau ]$.

When the stator is slotted, air gap magnetic field generated by the permanent magnet changed. Taking the whole number of slots as a whole, Fig. 3 shows the variation of the equivalent air gap length of the primary stator element of the motor with $x$ after the stator is slotted. The origin of coordinates is selected at the center point of the tooth groove of the primary stator element.

Fig. 3

Equivalent air gap length distribution of stator slotted

Within the range of $x \in [ - 3{\text{t}},3{\text{t}}]$, the equivalent air gap length changes with $x$ can be expressed as:

$$ \delta_{0} (x) = \left\{ {\begin{array}{*{20}c} {\delta ,kt \le x \le kt + \frac{b}{2}} \\ {\delta + h_{s} ,kt + \frac{b}{2} \le x \le kt + \frac{b}{2} + w} \\ {\delta ,kt + \frac{b}{2} + w \le x \le kt + b + w} \\ \end{array} } \right. $$

(7)

where: it is the tooth pitch, b is the groove width, w is the tooth width, h_s is the groove depth; k = 0, ± 1, ± 2, −3.

Order $d_{0} (x) = \frac{1}{{\delta_{0} (x)}}$, then there is:

$$ {\text{d}}_{0} (x) = \left\{ {\begin{array}{*{20}c} {\frac{1}{\delta },kt \le x \le kt + \frac{b}{2}} \\ {\frac{1}{{\delta + h_{s} }},kt + \frac{b}{2} \le x \le kt + \frac{b}{2} + w} \\ {\frac{1}{\delta },kt + \frac{b}{2} + w \le x \le kt + b + w} \\ \end{array} } \right. $$

(8)

The expression after the Fourier transform is:

$$ d_{e} (x) = \frac{1}{t}(\frac{w}{\delta } + \frac{b}{{\delta + h_{s} }}) + \sum\limits_{m = 1}^{\infty } {\left\{ {\frac{{2h_{s} }}{{\left( {\delta^{2} + \delta *h_{s} } \right)\pi m}}*\sin (\frac{n\pi *w}{t})\cos (\frac{2n\pi *x}{t})} \right\}} $$

(9)

Among them $x \in [ - 3{\text{t}},3{\text{t}}]$.

When the stator is slotted, since the air gap changes periodically and evenly, the permeability per unit area in the air gap is:

$$ \Lambda (x) = \frac{{\mu_{0} }}{\delta (x)} $$

(10)

When the stator is slotted, the air gap magnetic density generated by the permanent magnet can be expressed as:

$$ B(x) = \frac{{B_{\delta } (x)*\delta }}{\delta (x)} $$

(11)

In the type: $B(x)$ is the no-load air gap magnetic density under the stator slot; $B_{\delta } (x)$ is the no-load air gap magnetic density under unslotted stator.

Combining formula (8) and formula (11), the analytical formula of air gap magnetic density of the coupling part of the rotor at any position can be derived as follows:

$$ B_{{\text{e}}} (x) = \delta *d_{e} (x)*B_{\delta } (x - l) $$

(12)

where, $l$ is the distance of the polar center line offset from the center line of the tooth groove.

3.2 The Comparison of Air Gap Magnetic Density Analysis and Finite Element Method

In order to verify the validity of the above analytical derivation of the airgap magnetic field, two primary stator elements and a secondary actuator were used as the model, Ansoft Maxwell 2D was used for finite element simulation of the airgap magnetic density of the two-dimensional model. The situation when the actuator runs between the stator elements is shown in Fig. 4:

Fig. 4

Operation of the moving magnetic SPPMLSM a The mover is at the left end of two stator units b When the mover crosses two stator units c When the mover is coupled with a single stator unit

The electromagnetic field simulation function of Ansoft Maxwell 2D was utilized to conduct finite element two-dimensional numerical simulation of the magnetic density of the air gap between permanent magnet and primary stator element. The simulated results of the magnetic density of the air gap based on the three situations in Fig. 4 are shown in Fig. 5;

Fig. 5

Finite element analysis of air gap flux density of motor model a, b and c respectively correspond to the air gap magnetic density waveform of the mover at different positions in Fig. 4

It can be seen from Fig. 4 and 5 that the total coupling area between the two primary stator elements is unchanged when the stator is running, and the air gap flux density in the part of the moving stator coupled with each other is shown as an irregular shape waveform with a period of 42 mm, while the air gap flux density in the uncoupled part of the moving stator is shown as a more regular waveform with a period of 42 mm. The waveforms of the coupled and uncoupled parts of the stator are compared by the analytical formula method.

Figure 6 shows the comparison between the results of the no-load airgap magnetic density analysis method and the finite element method when the dynamic stator is partially coupled in the motor model, and the reliability is verified by using the harmonics of the air gap part. It can be seen that the analytical formula derived above can more accurately reflect the no-load airgap magnetic field when the dynamic stator is coupled.

Fig. 6

a Comparison between analytical method and finite element method for no-load air gap flux density of motor with dynamic stator coupling b Comparison between analytical method and finite element method for time–space carrier air gap harmonic analysis of dynamic stator coupling

When the secondary actuator runs between the segments of the primary stator element, the air gap magnetic density formula of the uncoupled part can be derived from the air gap magnetic density formula when the stator is not slotted, that is, the value of the air gap length $\delta$ is increased. When the air gap length is large, the situation is the same as that of the uncoupled part of the moving stator. Figure 7 shows the comparison of the results of the no-load airgap magnetic density analysis method and the finite element method in the motor model when the moving stator part is not coupled, and the air gap harmonic analysis is used to verify the results.

Fig. 7

a Comparison between analytical method and finite element method of the uncoupled no-load air gap magnetic density b Comparison of the results of the uncoupled no-load air gap harmonic analysis method and finite element method

According to the data shown in Fig. 6 and Fig. 7, there is a certain error between the analytical method and the finite element method of air gap harmonic analysis. In practice, because the magnetic permeability of the iron core is much greater than that of the air, and the magnetic density of the tooth groove or the edge of the end is affected by the change of the medium and the end effect, the magnetic density of the air gap increases abruptly. There is a difference between the analytical method and the finite element method in the direction of the magnetic field line in the tooth groove, so there will be some errors. Figure 7(a) shows that the 5th and 13th harmonics play a major role in the air gap magnetic density waveform through the simulation data of the finite element method. The amplitude of the number of major harmonics is effectively fitted by the analytical method, while the influence of the magnetic density of the air gap caused by the number of non-major harmonics is not fully fitted. In addition, only the first 10 harmonics were taken into account in the fitting with the finite element method in the analytical calculation, and the influence of the remaining harmonics on the magnetic density of the air gap was not fully considered. Therefore, there were errors in the two contrast curves in the image, namely the “burr” phenomenon in the curve of the analytical method.

4 Structure Optimization of SPPMLSM

The permanent magnet linear synchronous motor has obvious side end effect because the stator core is broken at both ends under static condition. And because the motor core is slotted, the tooth slotting effect is produced. The magnetic resistance of linear motor is composed of the groove force generated by the groove effect and the end force generated by the side end effect, which is the main reason for the thrust fluctuation of PMLSM. To improve the stability and reliability of the motor, we must try to reduce the magnetic resistance. When the secondary actuator moves in and out of the primary stator element, the finite element image of the magnetic resistance received by the actuator when it moves in and out of the primary stator element is shown in Fig. 8. As can be seen from the image, when the actuator enters and exits the stator, the end force is much greater than the tooth groove force. Therefore, this paper starts with the optimization of the motor body structure to reduce the end force of the actuator when running between segments.

Fig. 8

a Schematic diagram of moving in and out of single stator b Magnetic resistance of moving in and out of single stator

Because the basic structure of the moving magnetic segmented primary permanent magnet synchronous linear motor studied in this paper is L = L1 + L2, the secondary actuator is affected by two stator elements at the same time between the switching stator segments. It enters one stator element and leaves the other one at the same time, and the coupling area of the moving stator is unchanged. The actuator is subjected to both the end force in the opposite direction when leaving the stator and the end force in the same direction when entering the stator, which can partially cancel each other. The force situation is shown in Fig. 9. The comparison between Fig. 8 and Fig. 9 shows that the arrangement of L = L1 + L2 can reduce the magnetic resistance by 20%.

Fig. 9

a Two-dimensional model of PMLSM b Detent force of mover when switching between two stators

It can be seen from Fig. 9 (b) that the magnetic resistance of the actuator moving between segments is an odd function with the symmetry axis formed by the middle position of the two stator elements. In order to more clearly compare the weakening of each optimization model to the magnetic resistance with images, the finite element analysis of the magnetic resistance after structure optimization mainly analyzes the stress situation of $x \in [ - 84,0]$.

We try to install auxiliary teeth at both ends of the primary stator element to reduce the magnetic resistance of the actuator when switching between segments. After parametric analysis and finite element simulation, it is finally found that the rectangular auxiliary tooth with width of 9 mm, height of 47 mm and material of steel_1008 has the best effect on magnetic drag weakening. Figure 10 shows the proposed model of the stator auxiliary teeth. Compared with the basic model in Fig. 9, the flux resistance of the actuator during operation is reduced by 41.6% when the primary stator element model with the primary stator auxiliary teeth is used compared to the one without the addition.

Fig. 10

a Schematic diagram of the size of stator auxiliary teeth b The two-dimensional model of the motor with stator auxiliary teeth c Comparison of detent force' between primary optimization and original model

Adding auxiliary teeth to both ends of the primary stator on the initial model can play a significant role in the optimization. However, since the actuator is still subjected to a large magnetic resistance when switching between segments, further structural optimization is needed to reduce the end force caused by the primary stator breaking. Therefore, this paper attempts to optimize the structure of the secondary actuator back iron, adding auxiliary stages to both ends of the actuator back iron to reduce the magnetic resistance during operation, and using the finite element two-dimensional numerical analysis of the force value of the actuator when switching between stator segments. By adding different auxiliary stages at both ends of the movable back iron to optimize its structure, the proposed model of changing the shapes of both ends of the movable back iron to reduce the end force is shown in Fig. 11.

Fig. 11

a Model 1: Rectangular auxiliary level b Model 2: Wedge-shaped auxiliary stage c Model 3: Step-type auxiliary stage d Model 4: Cambered auxiliary stage

By comparing the basic model in Fig. 9 with the model of the stator auxiliary teeth in Fig. 10 and the four auxiliary stage models in Fig. 11, the finite element two-dimensional numerical simulation was carried out to test the weakening of the magnetic resistance caused by the addition of the moving auxiliary stage. Figure 12 shows the waveform of the magnetic resistance of the motors of each model when switching between segments. It can be seen from Fig. 12 that the superposition of the actuator auxiliary stage and the stator auxiliary teeth is extremely effective in weakening the magnetic resistance. Compared with the magnetic resistance in the original model, the magnetic resistance is reduced by 76% in the finite element analysis results under the joint action of stator auxiliary teeth and moving auxiliary teeth.

Fig. 12

Finite element comparison of detent force of various structures

As shown in Fig. 12, it can be proved that the magnetic resistance of the superposition effect of the actuator auxiliary pole and the stator auxiliary stage is smaller than that of the basic model and the proposed model with only the stator auxiliary teeth. The maximum magnetic resistance of the basic model is 51.44N, while the maximum magnetic resistance of the model with only stator auxiliary pole is proposed to be 27.32N. In the proposed model of superposition of stator auxiliary teeth and actuator auxiliary stages, the maximum magnetic resistance shown by the rectangular auxiliary stage of model 1 is only 12.5N.

Although the differences of magnetic drag values in various models can be compared in Fig. 12, it is difficult to judge the relative merits of each model. Therefore, energy conversion method is used to evaluate the effect of each model on magnetic drag weakening. The total energy value of each model's magnetic resistance after calculation is shown in Fig. 13. The energy is calculated as follows:

$$ W_{{\text{e}}} = \int {\left| {F_{{\text{c}}} (x)} \right|dx} $$

(13)

Fig. 13

Calculate the total detent force energy of each model by energy conversion

Fig. 14

Actuator motion process under rated load condition

where, We is the total energy of magnetic resistance received by the actor when switching between segments, and F_c(x) is the magnetic resistance received by the actor at the corresponding time $x$, and the integral interval is $x \in [ - 84,0]$。

In Fig. 13, the total magnetic resistance energy received by the moving segments of each model is 1691.18 J. The total magnetic resistance capacity of the model with only the stator auxiliary stage is 876.77 J, while that of model 1 with the minimum total magnetic resistance energy is only 389.79 J in the model with the stator auxiliary stage and the moving auxiliary teeth. By comparing the energy of the model with the superposition of the stator auxiliary teeth and the actuator auxiliary stages, it is found that the model with the rectangular auxiliary stages added at both ends of the secondary back iron can better reduce the magnetic resistance of the actuator when it moves between the stator segments.

5 Load Simulation Comparison of Motor Model Before and After Optimization

The first two parts of this paper are mainly based on the situation of the motor model under no-load, the electromagnetic characteristics of the no-load force of the motor before and after the structure optimization. As can be seen from Table 1, the rated working condition of the motor model studied in this paper is as follows: when the rated input current is 5.3 A, the actuator part of motor is subjected to rated thrust of 350 N and runs at the maximum speed of 1 m/s.

Under the rated load condition, the operation of the moving part is mainly divided into three processes: entering the stator, switching between the stator segments and leaving the stator. A two-dimensional numerical simulation model is constructed for the stator part composed of four discontinuous primary stators and the secondary permanent magnet as the moving part.

Using the simulation function of the force characteristics of the model with the finite element simulation software Ansoft Maxwell 2D, the dynamic parameters were set as the running speed was 1 m/s and the amplitude of three-phase AC current through the windings is 5.3 A. The thrust simulation under rated load was carried out on the original motor model before optimization and the motor optimization model after adding secondary auxiliary poles and primary auxiliary teeth. The thrust and thrust fluctuation of the two models in operation were explored, and the data were compared and analyzed.

As can be seen from Fig. 15, when the actuator enters the single-section stator, it will be attracted by the part of the stator, and the force will not become stable until the actuator is fully coupled with the single-section stator. When the two ends of the stator switch, there will be a large thrust fluctuation, which is the end force when the actuator enters and exits the stator section at the same time. In the process from coupling with the first stator to coupling with the last stator and not leaving ($x \in [0.3,1.3]$), the thrust force received by the actuator fluctuates basically with a certain value as the average value. This average value is the average thrust received by the actuator when it is running, and the fluctuation of thrust value is the manifestation of thrust fluctuation.

Fig. 15

Comparison of thrust of motor model before and after optimization

According to the curve in Fig. 15 and the data in Table 2, before optimization, the average thrust received by the actuator in the original motor model is close to the rated thrust. However, during the inter-segment switch, due to the influence of the side end force, the thrust fluctuation rate is as high as 30.8%, which makes the motor unable to operate normally. After the motor model is optimized, the average thrust received by the actuator and the stator is reduced compared with that before the optimization, which may be because the increase of mass caused by the addition of auxiliary stage in the secondary back iron part will lead to the decrease of thrust during operation. Due to the addition of primary auxiliary teeth and secondary auxiliary stages, the force of the motor will be more stable during operation, and the thrust fluctuation during intersegment switching will be weakened a lot. The fluctuation rate only accounts for 7.93%, indicating that the motor motion characteristics and force characteristics have been greatly improved after structural optimization compared with that before optimization. The structural optimization method tried in this paper is effective.

Table 2 Stress of the motor under rated working conditions before and after optimization

6 Conclusion

The research object of this paper is the primary moving magnetic discontinuous segmented permanent magnet synchronous linear motor. In order to solve the problem that the motor suffers too much magnetic resistance when switching between two stator segments, two-dimensional finite element simulation analysis is carried out on the motor model to understand its electromagnetic and mechanical characteristics, and structural optimization is carried out to reduce the magnetic resistance. By adding auxiliary poles to both ends of the primary stator element and auxiliary teeth to both ends of the moving magnetic backplane, the amplitude of the magnetic resistance is reduced from 52.3N to 12.5N, which effectively weakens the influence of the magnetic resistance without affecting the electromagnetic performance and makes the motor have a more stable and reliable operating condition. According to the finite element comparison simulation under the rated load condition, the motion characteristics and mechanical characteristics of the motor after optimization are greatly improved compared with that before optimization. This method does not change the effective area of the stator coupling, nor does it change the electromagnetic performance of the motor during operation. It not only improves and optimizes the structure design of the motor, but also provides the simulation basis for the switching part between the stator segments in the subsequent drive experiment.