KR20100080653A - Rotor and stator design method on torque ripple reduction for a concentrated winding synchronous reluctance motor and a rotor and stator designed by its method - Google Patents

Abstract

PURPOSE: A method for designing a rotor and a stator and the rotor and the stator designed by the same are provided to reduce a design cost by optimizing the design based on the design variables of the rotor and the stator. CONSTITUTION: A CAD(Computer Aided Design) file for designing a rotor and a stator is initialized. Data for a finite element modeling is set. The range of the design variables and the test frequencies are set by using a central composite design method. A torque ripple value is calculated by using a finite element analysis program. The design variable includes a slot open width(15), a slot depth(13), and a tooth width(14) of the stator and a magnetic flux barrier width(L1-L4) of the rotor.

Description

Rotor and Stator Design Method on Torque Ripple Reduction for a Design of Rotor and Stator for Torque Ripple Reduction of Concentrated Winding Synchronous Reluctance Motor Concentrated Winding Synchronous Reluctance Motor and A Rotor and Stator designed by its Method}

The present invention is to initialize and pre-process the CAD file to design the rotor and stator to reduce torque ripple based on the design variables of both the stator and the rotor, not the individual design of the stator or rotor related to the torque ripple of the central winding. After setting the pre-processor working data, because of manufacturing limitations, the rib width of the rotor is set to a fixed value, and the slot open width (X1), slot on the stator side affects torque ripple. After adopting the depth (X2), the tooth width (X3) and the magnetic flux barrier width (L1 to L4) as the design variables, the central composite design, one of the RSMs, which is a statistical approximation method: After setting the range of the design variable and the number of experiments using the CCD), the torque ripple value is calculated using the finite element analysis (FEA), and the calculated torque ripple value is recorded. Optimal rotor and stator design method for torque ripple reduction of intensive winding synchronous reluctance motor consisting of the steps of storing on the rotor and stator of the concentrated winding synchronous reluctance motor designed and manufactured by the design method It is about.

In general, synchronous reluctance motors (SynRM) have many advantages, such as higher efficiency and less manufacturing cost than induction motors.If stator windings of synchronous reluctance motors are conventional winding-type windings, When it is manufactured, the winding work is simplified during manufacturing, and the copper loss is reduced and the low-cost electric motor can be secured.

However, because vibration and noise generated by torque ripple are relatively higher than those of other devices, a proper combination of design variables should be made to reduce torque ripple.

Response surface methodology (RSM) is a statistical and mathematical method that can be used to find “optimal values” in the response studies of physical systems. In general, since polynomial models are created to represent the relationship between the design variables and the outputs within the response surface method, these models can be used to estimate the output, and design optimization can be performed more easily. The characteristics of a suitable model are assessed by identifying statistical tables based on experimental data.

Two research papers on SynRM have been published. First, there are stator designs based on stator width, slot open width, and slot depth as design variables to reduce torque ripple based on the rotor optimal design model of 24-slot SynRM. Second, based on the first stator optimization design. Therefore, there is a rotor design that performs optimal design using the number of magnetic flux barriers and the magnetic flux barrier width as design variables. Although the torque ripple could be reduced through this previous research and development, it is still difficult to commercialize it, and the physical characteristics of the concentrated winding type SynRM cannot be accurately predicted or improved by the individual design of the stator and the rotor. have.

The problem to be solved by the present invention is not the individual design of the stator or rotor of the central winding type SynRM, but the stator of the central winding type SynRM by performing the optimal design to reduce torque ripple based on the design variables of both the stator and the rotor. Alternatively, the rotor is designed and manufactured to reduce production costs and improve performance.

The problem to be solved by the present invention uses the response surface method (RSM), which is a statistical approximation method in designing and manufacturing the stator or rotor of the concentrated winding SynRM, and the response surface method always includes an error To determine the suitability of the design model by checking the degree of the approximation function of the rotor and the stator to perform the optimal design.

The problem to be solved by the present invention is to quickly and accurately estimate the response surface with a small number of experiments by applying the central synthesis planning method, one of the response surface method that is a statistical approximation method by adding the center point and the axial point to the 2 ^k factor experiment.

The problem solving means of the present invention is a rotor and stator of the central winding SynRM for reducing torque ripple based on the design parameters of both the stator and the rotor, not the individual design of the stator or the rotor associated with the torque ripple of the central winding SynRM Initializing the CAD file and setting up the pre-processor working data for the design. Due to manufacturing limitations, the rotor's rib width is set to a fixed value and the stator affects torque ripple. The response surface is a statistical approximation method through the steps of adopting the slot open width (X1), the slot depth (X2), the tooth width (X3) and the magnetic flux barrier width (L1 to L4) on the rotor side as design variables. After calculating the range of design variables and the number of experiments using the central synthesis planning method, which is one of the methods, and calculating the torque ripple value using the finite element analysis (FEA), A rotor and stator design method for reducing torque ripple of a concentrated winding synchronous reluctance motor comprising storing ripple values in a memory and a rotor and a stator of a concentrated winding synchronous reluctance motor designed and manufactured by the design method are provided. It is.

Another problem solving means of the present invention is that the design of the stator or rotor of the central winding type SynRM includes the error when applying the response surface method that is a statistical approximation method of the rotor and stator model of the designed concentrated winding SynRM A method of designing rotor and stator for reducing torque ripple of a concentrated winding synchronous reluctance motor equipped with means for determining the degree of estimated approximation function using analysis of variance (ANOVA) To provide.

Another problem solving means of the present invention is to apply the central synthesis planning method, which is one of the response surface method, which is a statistical approximation method that adds the center point and the axial point to the 2 ^k factor experiments in order to estimate the response surface with a small number of experiments. The present invention provides a method of designing a rotor and a stator for reducing torque ripple in a synchronous reluctance motor.

The present invention performs an optimal design to reduce torque ripple based on the design parameters of both the stator and the rotor, not the individual design of the stator or the rotor of the concentrated winding synchronous reluctance motor. The production cost is reduced, and the performance is improved.

Another effect of the present invention is to use the response surface method, which is a statistical approximation method in designing and manufacturing the stator or rotor of the concentrated winding SynRM, and the response surface method, which is a statistical approximation method, always includes an error. Optimal design is performed by checking the degree of approximation function of the rotor and stator of SynRM to determine the suitability of the design model.

Another effect of the present invention is to quickly and accurately estimate the response surface with a small number of experiments by applying the central synthesis planning method, one of the response surface methods, which is a statistical approximation method by adding the center point and the axial point to the ^2k factor experiment.

Hereinafter, the present invention will be described in detail. The present invention provides the CAD file of the initial starter to design the rotor and stator to reduce torque ripple based on the design variables of both the stator and the rotor, not the individual design of the stator or rotor related to the torque ripple of the central winding. After setting the preprocessing work data, due to manufacturing limitations, the rib width of the rotor is set to a fixed value, and the slot open width (X1) and slot depth (X2) on the stator side affecting torque ripple. ), The tooth width (X3) and the magnetic flux barrier width (L1 to L4) on the rotor side are adopted as the design variables, and the central composition planning method, which is one of the response surface methods, is a statistical approximation method. After setting the range and the number of experiments, calculating the torque ripple value using the finite element analysis (FEA), and storing the calculated torque ripple value in the memory The present invention relates to a rotor and stator for a torque ripple reduction of a concentrated winding synchronous reluctance motor, and a rotor and stator of a concentrated winding synchronous reluctance motor designed and manufactured by the design method.

Hereinafter, the configuration and operation of the embodiments of the present invention with reference to the accompanying drawings, the configuration and operation of the present invention shown and described in the drawings will be described by at least one embodiment, whereby the present invention described above The technical idea and its core composition and operation are not limited.

Look at the drawings to facilitate understanding of the present invention. 1 illustrates design variables of a concentrated winding SynRM according to the present invention, and FIG. 2 illustrates change point variables and a change direction of a rotor according to the present invention. FIG. 3 shows the change point variables and the direction of change of the stator. FIG. 4 shows the basic concept of the response surface method. Figure 5 shows a flow chart of the design procedure according to the present invention, Figure 6 shows a comparison of the initial model and the optimal model for the stator design. FIG. 7 shows a comparison between the initial model and the optimal model for the rotor design, and FIG. 8 illustrates the comparison between the initial model and the optimal model for the stator and rotor design. Figure 9 shows the analysis results of the torque ripple calculated according to the design method of the concentrated winding SynRM stator and rotor according to the present invention. A specific embodiment according to the present invention will be described.

EXAMPLES

A specific embodiment according to the present invention will be described with reference to the drawings. The analytical models of the synchronous winding SynRM (Synchronous Reluctance Motor) according to the present invention are four poles and six slots. The lamination length is 77 (mm), the rotor diameter is 30.1 (mm), the void is 0.4 (mm), and the stator diameter is 87.9 (mm). As shown in FIG. 1, design variables related to torque ripple of the concentrated winding SynRM include a slot of a stator, an air gap 16, a rib width of a rotor 11, a number of magnetic flux barriers, and a magnetic flux barrier width. In the present invention, the optimal design of the central winding SynRM is made by the slot open width (15, X1) of the stator side, the slot depth (13, X2), the tooth width (14, X3) and the magnetic flux barrier width (L1 to L4) of the rotor side. Adopt as a variable for. Figure 2 shows the change point variable and the change direction for the shape change according to the magnetic flux barrier width in the number of three magnetic flux barriers. (W1, W8), (W2, W7), (W3, W6), which are each paired. … Moves symmetrically about the q-axis. The points P1-P5 move in a state that varies with the flux barrier width. 3 shows a change point variable and a change direction for shape change according to each variable on the stator side.

Figure 4 shows the basic conceptual diagram of the response surface method (RSM) used in the stator and rotor design of the concentrated winding SynRM. The response surface method finds the relationship between the design variables and the response and uses the observed data to find the response to the stator and rotor model of the optimal concentrated winding type SynRM using statistical approximation. Here, the response or output value corresponding to the design variable is generally obtained through actual experiment or computer simulation, and the actual response value is composed of expected value or average value.

Therefore, in the present invention, observation data were acquired through a finite element method by computer simulation for the correspondence between design variables and output values. In response surface methodology (RSM), the actual response y for k design variables is assumed as follows.

              y = f (X, θ) (1)

In equation (1), the variables (x ₁ , x ₂ , .... x _k ) are natural variables and have actual units of measure. The approximate function y of the actual response function f is approximated by a first- or second-order polynomial model based on the Taylor series.

Since the response surface of the study object selected in the present invention can be predicted to be represented by a curved surface, an approximation function was used as a quadratic model. Therefore, the relationship between the actual response function f and the approximation function y can be expressed as Equation (2).

(2)

ε is the error term of the response, and variable is the code variable. Here, we treat ε as a statistical error and generally assume a normal distribution with a mean of 0 and a variance σ ² . Therefore, the output value y estimated from n sample data from the approximation function is summarized as Equation (3) in the form of a matrix.

y = Xβ + ε (3)

는 식(4)과 같다.Where X is a matrix of design variable levels, β is a vector of regression coefficients, and ε is a vector of random error. And the function estimated in equation (3)

Is as shown in equation (4).

=Xb (4)

= Xb (4)

There are many experimental design methods in the response surface method (RSM) used in the stator and rotor design of the concentrated winding SynRM of the present invention. In order to confirm the approximation of the estimated approximation function in the present invention, a central composite design (CCD) was used, which is the most commonly used method for response surface design.

의 계수

등을 추정할 수 없다.2 ^k factor experiments (2 ^k factorial experiments) is not able to detect a surface change of the reaction volume is generated in accordance with the level change of the variable two-level (plane) only in the experiment because of the variables, the secondary of the formula (2) Square term in polynomial regression model

Coefficient of

Cannot be estimated.

In order to make up for the shortcomings and to estimate the response surface with a small number of experiments, the experimental plan that adds the center point and the axial point to the 2 ^k factor test is called the central composition planning method.

Table 1. ANOVA

The response surface method, which is a statistical approximation method, always contains an error, and the central synthesis planning method, which is one of the response surface methods, which is a statistical approximation method, also includes an error. Therefore, the error degree of the estimated approximation function must be checked after designing. . In the present invention, the analysis of variance (ANOVA) was used to confirm the error degree of the estimated approximation function. In Table 1, n is the total number of experiments, and k represents the number of design variables for the appropriate model. . Next, there are three error sums (SS _E ), the sum of squares of total deviations (S _yy ), and the regression sum of squares (SS _R ) that play an important role in determining the model's suitability.

The residual sum of squares is SS _E , the sum of squares of the total deviations is S _yy , and the regression sum of squares SS _R = S _yy -SS _E.

here,

i: 예측 값,

: 평균 값) (yi: observed value,

i: predicted value,

: Average value)

The crystal coefficient R ² is S _yy and SS _R , and is represented by Equation (5).

(5)

(5)

The coefficient of determination is the percentage of total variation that is accounted for by the regression line. The correction coefficient for modifying R ² is

(6)

(6)

)은 총 평균제곱에 이용되는 추정된 오차분산 값을 분모로 하고, 잔차 평균제곱에 의하여 제공된 추정된 오차분산 값을 분모로 하여 얻은 값이다. 그러므로 회귀선의 타당성은 결정계수(R ² )과 수정결정계수(

)에 의하여 결정된다. 도 5는 본 발명에 따른 집중권선 SynRM의 고정자와 회전자의 모든 설계변수를 기초로 토크리플을 저감하기 위한 집중권선 SynRM의 회전자와 고정자 설계의 흐름도를 나타낸 것이며, 도 5의 설계 흐름도에 나타난 본 발명에 따른 회전자 및 고정자 설계방법을 순서에 기초하여 기술하면 다음과 같다. As shown in Table 1, the mean square is the sum of squares divided by the degrees of freedom. Equation (6) is the total mean squared (S _yy / n-1), and the measure ratio (

) Is a denominator of the estimated error variance used for the total mean square, and the denominator of the estimated error variance provided by the residual mean square. Therefore, the validity of the regression line is that the coefficient of determination ( R ² ) and the correction coefficient (

Is determined by FIG. 5 shows a flow chart of the rotor and stator design of the central winding SynRM for reducing torque ripple based on all design variables of the stator and rotor of the central winding SynRM according to the present invention. The rotor and stator design method according to the present invention will be described based on the sequence.

1. It is a step to set up data for finite element modeling by computer aided design (CAD) file initialization and pre-processor work.

The preprocessing work data is to model the design data for finite element analysis of the structure required for the rotor and stator design to reduce torque ripple.

2. The design variables of the rotor and stator to reduce the torque ripple include the slot open width (X1), slot depth (X2), tooth width (X3) and magnetic flux on the rotor side of the stator, which affect the torque ripple. The barrier widths L1 to L4 are adopted, and the rib width of the rotor is set to a fixed value due to manufacturing limitations.

3. In the present invention, among the many experimental design methods of the response surface method, the range of design variables and the number of experiments are set by using the central synthesis planning method as shown in Tables 2 and 4. The number of experiments N in the embodiment of the present invention was set from 1 to 90.

4. It is the step of calculating torque ripple value of concentrated winding type SynRM using the program for finite element analysis (FEA) developed for stator and rotor design of concentrated winding synchronous reluctance motor.

5. This is a step of storing torque ripple value calculated from FEA by developed program.

The finite element is given in the form of a small lattice, and the generated lattice is called a mesh, a point forming a vertex of the mesh is called a node, and an area of the mesh connected by the node is called an element. do.

Regarding the design of the rotor using the finite element analysis, it is disclosed in Korean Patent Publication No. 10-0709296, which is filed and registered by the applicant in 2005.

6. It is a step of checking (N> 90?) When the number of experiments N is set to 90.

When N is larger than 90, the optimum torque ripple is considered. When N is smaller than 90, the torque ripple value is continuously calculated by adding 1 to the N value.

7. The change point variables and the change direction for the shape change according to the design variables of the stator and the rotor are shown in FIGS. 2 and 3.

When analyzing the changed stator and rotor shape according to the change of design variables (X1, X2, X3, L1 to L4), it is difficult to perform many pretreatment work for finite element analysis.

For this reason, CAD files are automatically programmed to be redrawn for changes in flux barrier width. Next, meshing is automatically remeshed. Here, only the x and y coordinates of the rotor change at the same number of magnetic flux barriers, and the node number, element number, boundary condition, and the like do not change.

This automatic shape change program is included in the design program of the present invention to design and execute the program, thereby reducing the design time. This experimental procedure is performed up to N = 90.

8. Based on the design variables and the range of the experimental period, the model of response surface was formed and the optimal torque ripple was investigated by the data obtained through the finite element analysis.

Table 2 shows the range of design variables by the central synthesis planning method among many experimental design methods of the response surface method, and Table 3 shows the response values of finite element analysis based on the design variables in Table 2. The torque ripple shown in Table 3 was obtained by the finite element method. Using these experimental results, the second order polynomial

=3307.08-53.99X1-17.04X2+21.71X3-1401.44L1+.....-31.46L4-48.901L3L4 (7)

= 3307.08-53.99X1-17.04X2 + 21.71X3-1401.44L1 + .....- 31.46L4-48.901L3L4 (7)

=0.887에서 총 변동 88.7%는 이는 80% 이상이므로 적합한 모델임을 식 (7)에 의하여 설명되어 질 수 있다는 것을 나타내고, 잔차 평균제곱에 의해 제공된 잔차 변동의 추정은 표1의 수식에서 총 평균제곱을 분모로 하고, 잔차 평균제곱을 분자로 하여 얻은 것으로 11.3%이다.Table 4 shows the results of the variance analysis performed according to the equation given in Table 1 to determine the suitability of the designed model by checking the error degree of the estimated approximation function. Since F ₀ = 20.01 exceeded F _(35,53,0.05) = 0.1561, the invalid hypothesis that all coefficients β represent 0 is rejected. With R ² = 0.892

At 0.887, the total variance 88.7% indicates that this is a suitable model because it is more than 80%, and the estimation of the residual variance provided by the residual mean square gives the total mean square in the formula in Table 1. It was obtained as the denominator and the residual mean square was found as the numerator, which is 11.3%.

Table 2. Scope of design variables

Table 3. Experimental Results Using Central Synthetic Planning

X1: slot open width, X2: slot depth, X3: tooth width, L1: flux barrier 1, L2: flux barrier 2, L3: flux barrier 3, L4: flux barrier 4, T _peak : peak-peak torque (Nm) , T _ave : average Torque (Nm) T _ripple : T _peak / T _ave (%)

Table 4. ANOVA

The suitability analysis and analysis of stator and rotor models of central winding SynRM for reducing torque ripple designed according to the present invention will be described. Fig. 6 and Fig. 7 show the comparative shapes of the initial model and the optimally designed model for the stator and rotor design of the 6-slot model, respectively, and Fig. 8 shows the initial and optimal design of the stator and rotor design of the central winding SynRM. The comparative shape of the model is shown. As shown in Fig. 9, the torque ripple of the optimally designed concentrated winding SynRM is larger than the conventional 24-slot model considering the variables (X1, X2, X3, L1 to L4) of both the stator and the rotor of the central winding SynRM. Smaller torque ripple was obtained than that of the individual stator design model (109.8%) and rotor design model (63.8%).

The number of magnetic flux barriers is 5 and X1 is 2.00 [mm], X2 is 14.00 [mm], X3 is 14.00 [mm], L1 is 3.564 [mm], L2 is 1.653 [mm], L3 is 2.253 [mm], and L4 is 3.033. At [mm], the torque ripple of the concentrated winding SynRM is minimal (56.3%), as shown in Figs. As a result, the torque ripple (56.3%) of the stator and rotor design models was significantly closer to the 24-slot model (48.3%) than the torque ripple of the individual design models of the stator and rotor.

Accordingly, the present invention provides an optimal design method using the response surface method to reduce the torque ripple of the concentrated winding SynRM. In order to reduce the production cost and improve the performance of the concentrated winding SynRM, the optimum design was designed to reduce torque ripple based on the design variables of both the stator and the rotor, not the individual design of the stator or the rotor. In order to speed up the design, the CAD program automatically creates the CAD file according to the shape change and the preprocessing program is included in the design program to reduce the design time. Starting from the existing design, the optimal design values were chosen, which would be important data for similar motor design. RSM can also be considered as a good means for optimal design of SCR and other devices.

The present invention provides the CAD file of the initial starter to design the rotor and stator to reduce torque ripple based on the design variables of both the stator and the rotor, not the individual design of the stator or rotor related to the torque ripple of the central winding. After setting the preprocessing work data, due to manufacturing limitations, the rib width of the rotor is set to a fixed value, and the slot open width (X1) and slot depth (X2) on the stator side affecting torque ripple. ), The width of the variable (X3) and the width of the magnetic flux barrier (L1 to L4) on the rotor side. Through the step of calculating the torque ripple value using the finite element analysis (FEA), the concentrated consisting of the step of storing the calculated torque ripple value in the memory Line synchronous reluctance provide a rotor and a stator design method according to the torque ripple reduction of reluctance motors because it is very high industrial applicability because it can reduce production costs and increase performance.

1 is a diagram showing design parameters of a concentrated winding SynRM according to the present invention.

2 is a view showing the change point variable and the change direction of the rotor according to the present invention

3 is a diagram showing change point variables and direction of change of the stator;

4 shows the basic concept of the response surface method.

5 is a flow chart of a design procedure according to the present invention

Fig. 6 shows a comparison of the initial model and the optimal model for the stator design

7 shows a comparison of the initial model and the optimal model for the rotor design.

8 shows a comparison of an initial model and an optimal model for the stator and rotor design.

9 is a diagram showing an analysis result of a torque ripple calculated according to a design method of a concentrated winding SynRM stator and a rotor according to the present invention.

<Description of the symbols for the main parts of the drawings>

11; Rib 12; roter segment

13; Slot depth (X2) 14; Tooth width (X3)

15; Slot open width (X1) 16; Air gap

L1-L4; Magnetic flux width on the rotor side

Claims (7)

In the rotor and stator design method for reducing torque ripple based on the design variables of the concentrated winding synchronous reluctance motor, Initializing the CAD file to design a rotor and a stator for reducing torque ripple; The lip width of the rotor is set to a fixed value, and it is designed for finite element analysis by adopting the slot open width, slot depth, tooth width, and magnetic flux barrier width on the rotor side that affect torque ripple as design variables. Modeling the data; Setting a range of design variables and the number of experiments using the central synthesis planning method, which is one of the reaction surface methods, which is a statistical approximation method; And Design of rotor and stator for reducing torque ripple of concentrated winding synchronous reluctance motor consisting of calculating torque ripple using finite element analysis program designed for rotor and stator design of central winding synchronous reluctance motor Way. The method according to claim 1, Torque ripple values obtained by setting and inputting the design variables include the error in the central composition planning method. Therefore, the suitability of the rotor and stator model of the concentrated winding synchronous reluctance motor designed by checking the error degree of the estimated approximation function The rotor and stator design method for reducing torque ripple of a concentrated winding synchronous reluctance motor, characterized in that the determination is made by analysis of variance. The method according to claim 2, The validity of the regression line in the analysis of variance used to check the degree of error is the coefficient of determination ( R ² )

Rotor and stator design method for reducing the torque ripple of the concentrated winding synchronous reluctance motor, characterized in that consisting of. The method according to claim 1, Finding the relationship between the design variable and torque ripple through computer simulation, focusing on applying central synthesis planning method with center point and axial point added to factor test in order to estimate the response surface with a small number of experiments Rotor and stator design method to reduce torque ripple of winding synchronous reluctance motor. The method according to claim 1, When analyzing the stator and rotor shape of the changed concentrated winding synchronous reluctance motor according to the change of the design variables (X1, X2, X3, L1 to L4), only the x and y coordinates of the rotor change at the same flux barrier number. A rotor and stator design method for reducing torque ripple of a concentrated winding synchronous reluctance motor, characterized by not changing the node number, element number, and boundary condition. The method according to claim 2, Central winding synchronization characterized in that the error is used to determine the suitability of the model is selected by using one or more of the sum of the residual square sum (SS _E) , the sum of squares of the total deviation (S _y ), and the regression sum of squares (SS _R ). Rotor and stator design method to reduce torque ripple of reluctance motor. The rotor and stator of the concentrated winding synchronous reluctance motor manufactured by the method of designing the rotor and stator of the concentrated winding synchronous reluctance motor for reducing torque ripple of the lumped winding synchronous reluctance motor according to any one of claims 1 to 6. .

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