CN113312768B - Optimization design method for electromagnet multi-quality characteristic parameters based on Taguchi and BBD - Google Patents
Optimization design method for electromagnet multi-quality characteristic parameters based on Taguchi and BBD Download PDFInfo
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Abstract
The technical scheme discloses an electromagnet multi-quality characteristic parameter optimization design method based on Taguchi and BBD, and relates to the field of electromagnet design quality, and the method comprises the following steps: A. selecting relevant design parameters, and designing and selecting a proper factor design level table by using a Taguchi method; B. calculating the signal to noise ratio of electromagnetic attraction force and temperature rise in each group of combined tests in orthogonal tests provided by Box-Behnken (BBD) response surface analysis; C. establishing a quadratic mathematical model between the BBD and each factor and verifying the validity of the model; D. and combining the maximum electromagnetic suction value and the minimum temperature rise value as optimization indexes to obtain the optimal quality characteristic parameter combination and carrying out experimental verification. The technical scheme has the advantages of improving the calculation speed and being excellent in time complexity and convergence.
Description
Technical Field
The technical scheme relates to the field of electromagnet design quality, in particular to a parameter optimization design method for multi-quality characteristics of electromagnets.
Background
The electromagnet is widely applied in automatic production, is a component for realizing electric energy-magnetic energy-mechanical energy conversion, and has the main advantages of small size, simple operation, preferential price and low driving force. The prior electromagnet has little demand, but with the development of economy, the electromagnet is taken as an important component in automatic control, and the demand of a plurality of enterprises for the electromagnet is larger and larger, and the quality requirement of the enterprises is also stricter. The mass design of the electromagnet is a critical part thereof, which places higher demands on the designer and producer of the electromagnet. The multi-quality characteristic of the electromagnet design stage is an important basis for determining the quality of the electromagnet design. Therefore, the problem of optimizing the multi-quality characteristics is to be controlled in the design process of the electromagnet, so that the quality of the electromagnet is in a good controlled state.
Disclosure of Invention
In order to overcome the defects of the background technology, the technical scheme provides the optimization design method for the multi-quality characteristic parameters of the electromagnet based on the Taguchi and the BBD, which is excellent in time complexity and convergence, and improves the calculation speed.
The technical scheme adopted by the technical scheme is as follows: the optimized design method of the electromagnet multi-quality characteristic parameters based on Taguchi and BBD comprises the following steps:
A. selecting relevant design parameters, and designing and selecting a proper factor design level table by using a Taguchi method;
B. calculating the signal to noise ratio of electromagnetic attraction force and temperature rise in each group of combined tests in orthogonal tests provided by Box-Behnken (BBD) response surface analysis;
C. establishing a quadratic mathematical model between the BBD and each factor and verifying the validity of the model;
D. and combining the maximum electromagnetic suction value and the minimum temperature rise value as optimization indexes to obtain the optimal quality characteristic parameter combination, and carrying out experimental verification.
In the step A:
according to the self characteristics of the electromagnetic brake, determining two mutually related mass characteristics of maximum electromagnetic force and temperature rise of the electromagnetic brake as analysis objects, wherein the maximum electromagnetic force is a hopeful characteristic, and the temperature rise is a hopeful characteristic;
combining electromagnet parameter analysis, selecting the inner diameter of the iron pivot, the width of the coil, the height of the spool and the diameter of the enameled wire as controllable factors of a Taguchi orthogonal experiment;
calculating the level value of each influence factor according to the following three-level formulation formula:
wherein ε 1 、∈ 2 、∈ 3 Three horizontal values representing controllable factors, respectively; e is the central level value of each factor; θ is the standard deviation of each factor, taking θ=0.1 e.
The step B comprises the following steps:
b1, correlating the two quality characteristics by using Taguchi and BBD analysis to obtain the optimal parameter design optimization combination.
B2, analyzing by adopting worst condition N1 and standard condition N2; obtaining the quality characteristic value in the orthogonal design combination analyzed by the BBD response surface through JMAG simulation and converting the quality characteristic value into a corresponding SNR value; the signal-to-noise ratio formula of the hope small characteristic is as follows:
(2) The signal-to-noise ratio formula of the telescopic characteristic is as follows:
(3) The signal-to-noise ratio formula of the eye observation characteristic is as follows:
wherein sigma andstandard deviation and mean values for the quality characteristics y; MSD is the mean variance of the quality characteristics.
The step C comprises the following steps:
c1, BBD response surface model selection,
B, designing and combining the step A according to a BBD orthogonal test method, and utilizing Design-expert11.0 software to arrange a BBD response surface Design table;
under the general condition that P is less than 0.05, according to the Design-expert11.0 software, the variance analysis is carried out on various models established based on the electromagnetic suction signal-to-noise ratio and the Wen Shengxin noise ratio respectively, and the model is obvious. And selecting a high-order model with effective and remarkable additional terms according to BBD selection models.
C2, BBD mathematical model establishment,
Fitting the relation between the quadratic function pair variable and the target variable according to a least square method by using Design-expert11.0 software to obtain a response function;
c3, BBD mathematical model response analysis,
The quadratic response mathematical model is established reliably according to the analysis of variance, which verifies that the quadratic model is significant.
The step D comprises the following steps:
aiming at the electromagnetic suction force of the telescope index, when optimizing, all factors need to be optimized to maximize the electromagnetic suction force; the temperature rise belongs to the index of the hope subclass, and when optimization is carried out, all factors are required to be optimized to enable the temperature rise to reach the minimum value; it is therefore necessary to set a maximum value where electromagnetic force cannot be achieved and a minimum value where temperature rise cannot be achieved.
The beneficial effects of this technical scheme are: analyzing the quality characteristic index of the electromagnet by using a parameter optimization design method of the multi-quality characteristic of the electromagnet, quantitatively calculating and qualitatively analyzing, selecting relevant design parameters, and designing and selecting a proper factor design level table by using Taguchi; calculating the signal to noise ratio of each group of combined tests in the orthogonal tests provided by Box-Behnken (BBD) response surface analysis of electromagnetic attraction force and temperature rise; and establishing a quadratic mathematical model between the BBD and each factor, verifying the effectiveness of the model, combining the maximum electromagnetic suction value and the minimum temperature rise value as optimization indexes, obtaining the optimal quality characteristic parameter combination, and performing experimental verification. The method has the advantages of improving the calculation speed and enabling the evaluation result to be more accurate, so that the method is superior to other methods in time complexity and convergence.
Drawings
Fig. 1 is a flow chart of an electromagnet multi-quality characteristic parameter optimization design method based on Taguchi and BBD according to an embodiment of the present disclosure.
FIG. 2 is d and l 1 A contour plot of the influence on the electromagnetic attraction signal-to-noise ratio.
FIG. 3 is d and l 2 A contour plot of the influence on the electromagnetic attraction signal-to-noise ratio.
FIG. 4 is l 1 And/l 2 A contour plot of the influence on the electromagnetic attraction signal-to-noise ratio.
FIG. 5 is l 2 And/l 3 A contour plot of the influence on the electromagnetic attraction signal-to-noise ratio.
FIG. 6 is d and l 1 A contour plot of the impact on Wen Shengxin to noise ratio.
FIG. 7 is a diagram of d and l 2 A contour plot of the impact on Wen Shengxin to noise ratio.
FIG. 8 is l 1 And/l 2 A contour plot of the impact on Wen Shengxin to noise ratio.
FIG. 9 is l 2 And/l 3 A contour plot of the impact on Wen Shengxin to noise ratio.
Fig. 10 is a simulation analysis chart of electromagnetic attraction force under different parameter values.
FIG. 11 is a graph of temperature rise simulation analysis for different parameter values.
Detailed Description
The following further describes embodiments of the present technical solution with reference to the accompanying drawings:
as shown in the drawings, the following further describes embodiments of the present technical solution with reference to the accompanying drawings:
under the condition that the design parameters in the early design process of the electromagnet are uncertain, the design parameters in the early design process are determined by using Taguchi and BBD response surface analysis.
Taguchi and BBD response surface analysis algorithm derivation procedure:
(1) Taguchi method
The fluctuation analysis of the electromagnet multi-mass characteristics of the maximum electromagnetic attraction force F and the maximum electromagnetic attraction force temperature T is combined with the electromagnet parameter analysis, and the inner diameter d of the armature (magnet) is selected 1 Coil width l 1 Spool height l 2 Diameter d of enamelled wire 2 The method comprises the steps of carrying out a first treatment on the surface of the Calculating the level value of each influence factor according to a three-level formulation formula (1):
wherein ε is 1 、∈ 2 、∈ 3 Three horizontal values representing controllable factors, respectively; e is the central level value of each factor; θ is the standard deviation of each factor, and θ=0.1∈ is taken in the technical scheme.
The Taguchi method is proposed by Tian Kouxuan-doctor, the signal-to-noise ratio (SNR) is an analysis index commonly used in the method, and certain problems exist in the process of calculating the signal-to-noise ratio, so that many scholars go to study, and a correction calculation formula of the signal-to-noise ratio of the objective characteristic is proposed:
wherein MSD is the mean square error of the quality characteristics.
The signal to noise ratio calculation is well-varied according to the difference of the properties of the multi-quality characteristics of the electromagnetic product.
(1) Small observation characteristics:
wherein sigma is sum ofIs the standard deviation and the mean with respect to the quality characteristic y.
(2) The telescope characteristic is as follows:
(3) The eye-observing characteristic is as follows:
when different quality characteristics are faced, different expressions are selected for calculation, and the optimal parameters are obtained.
(2) BBD response surface analysis
Step one: selection of BBD response model
The BBD is one of response surface analysis, and its main characteristic is that the values of all factors do not exceed the upper limit or lower limit of the set level. Considering the whole experiment as a cube, the BBD takes each experimental group point at the midpoint of each side
BBD response surface analysis other response surface analyses have fewer combinations than trial. BBD response surface analysis did not arrange all levels of the combinatorial trial to be either high or low, and it was in no regular order, with approximate rotatability.
And designing and analyzing a BBD response surface Design table according to the BBD orthogonal test method, and arranging the BBD response surface Design table by using Design-expert11.0 software.
Under the general condition that P is less than 0.05, according to the Design-expert11.0 software, the variance analysis is carried out on various models established based on the electromagnetic suction signal-to-noise ratio and the Wen Shengxin noise ratio respectively, and the model is obvious. And selecting a high-order model with effective and remarkable additional terms according to BBD selection models.
Step two: BBD mathematical model establishment
From the analysis of step one, the mathematical model is finally determined. And fitting the relation between the quadratic function and the variable and the target variable according to a least square method by using Design-expert11.0 software. A response function is obtained.
Step two: BBD mathematical model analysis
The quadratic response mathematical model is established reliably according to the analysis of variance, which verifies that the quadratic model is significant. And after determining a single factor, the influence of other factors on the target index is specifically analyzed.
(3) Simulation experiment verification
In the technical scheme, aiming at the electromagnetic suction force of the telescope index, all factors need to be optimized to maximize the electromagnetic suction force when optimizing. The temperature rise belongs to the index of the hope subclass, and each factor needs to be optimized to enable the temperature rise to reach the minimum value when the optimization is carried out. It is therefore necessary to set a maximum value where electromagnetic force cannot be achieved and a minimum value where temperature rise cannot be achieved.
The electromagnet influence factor level configuration table is formulated according to the size range required by the customer and the formula (1) as shown in the table 1.
Table 1 table of the level configuration of the influence factors of the electromagnet
In addition, in order to minimize the number of tests, the present solution uses worst condition N1 and standard condition N2 for analysis. This quality characteristic value in the orthogonal design combination of BBD response surface analysis is obtained through JMAG simulation and converted into a corresponding SNR value as shown in table 2.
Table 2 JMAG simulation and BBD orthogonal test combined quality characterization SNR values (dB)
Wherein, for the first set of combinations, it is available according to equation (4): from equation (3):
other data can be calculated in the same way.
The BBD is one of response surface analysis, and its main characteristic is that the values of all factors do not exceed the upper limit or lower limit of the set level. Considering the whole experiment as a cube, the BBD takes each experimental set point at the midpoint of each side,
BBD response surface analysis other response surface analyses have fewer combinations than trial. BBD response surface analysis did not arrange all levels of the combinatorial trial to be either high or low, and it was in no regular order, with approximate rotatability.
Wherein tables 3 and 4 show that the model is significant when P < 0.05 is typical for a plurality of model anova established based on electromagnetic suction signal to noise ratio and Wen Shengxin to noise ratio, respectively, according to Design-expert11.0 software. And selecting an effective and remarkable high-order model of the additional item according to the BBD selection model as much as possible.
TABLE 3 multiple model analysis of variance based on electromagnetic suction signal to noise ratio
TABLE 4 temperature rise signal to noise ratio based multiple model analysis of variance
From tables 3 and 4, the present solution selects a quadratic mathematical model for the Wen Shengxin-to-noise response model.
From the above analysis, it is known that the quadratic mathematical model is finally determined as the final response model. And fitting the relation between the quadratic function and the variable and the target variable according to a least square method by using Design-expert11.0 software. The response function is obtained as follows:
wherein the response functional relation expression between the electromagnetic suction signal-to-noise ratio F and Wen Shengxin-to-noise ratio T and each factor is expressed in the form of factor codes
Wherein the expression of the response function relation between the electromagnetic suction signal-to-noise ratio F and Wen Shengxin-to-noise ratio T and each factor is expressed in the form of actual factor values
From tables 5 and 6, the quadratic model is remarkable, and the establishment of the quadratic response mathematical model is reliable.
TABLE 5 quadratic model analysis of variance based on electromagnetic force signal to noise ratio
TABLE 6 quadratic model analysis of variance based on temperature rise signal to noise ratio
When the spool is at height l with respect to FIG. 2 2 And diameter d of enamelled wire 2 When the electromagnetic attraction signal-to-noise ratio is constant, the coil width l is increased along with the increase of the inner diameter of the iron pivot 1 The need for a decrease and an increase. When the coil width l is as for fig. 3 1 And diameter d of enamelled wire 2 When the electromagnetic attraction signal-to-noise ratio is constant, the height l of the spool is increased along with the increase of the inner diameter of the iron pivot 2 The need for a decrease and an increase. When the armature inner diameter d is as shown in FIG. 4 1 And diameter d of enamelled wire 2 When the electromagnetic attraction signal-to-noise ratio is constant, the electromagnetic attraction signal-to-noise ratio is kept constant along with the coil width l 1 Is increased by the spool height l 2 It is required to decrease and then increase. When the armature inner diameter d is as shown in FIG. 5 1 And coil width l 1 When the electromagnetic attraction signal-to-noise ratio is constant, the electromagnetic attraction signal-to-noise ratio is kept constant along with the height l of the spool 2 Is increased by the diameter d of the enameled wire 2 An increase is required.
When the spool is at height l with respect to FIG. 6 2 And diameter d of enamelled wire 2 When the coil is fixed, if the signal-to-noise ratio of the temperature rise is kept to be a certain fixed value, the coil width l is increased along with the increase of the inner diameter of the iron pivot 1 The need for a decrease and an increase. When the coil width l is as for fig. 7 1 And diameter d of enamelled wire 2 When the temperature is fixed, if the signal to noise ratio of the temperature rise is kept to be a certain fixed value, the height l of the spool is increased along with the increase of the inner diameter of the iron pivot 2 The need for a decrease and an increase. Powering on with respect to FIG. 8Pivot inner diameter d 1 And diameter d of enamelled wire 2 When the coil is fixed, if the signal-to-noise ratio of the temperature rise is kept to be a certain fixed value, the signal-to-noise ratio is kept unchanged along with the width l of the coil 1 Is increased by the spool height l 2 It is necessary to decrease and then increase. When the armature inner diameter d is as shown in FIG. 9 1 And coil width l 1 When the temperature is constant, if the signal to noise ratio of the temperature rise is kept to be a certain fixed value, the temperature rise is kept unchanged, and the temperature rise is kept to be equal to the height l of the spool 2 Is increased by the diameter d of the enameled wire 2 An increase is required.
Aiming at the electromagnetic attraction of the telescope index, various factors need to be optimized to maximize the electromagnetic attraction when optimizing. And the temperature rise belongs to the index of the hope subclass, and when the optimization is carried out, all factors are required to be optimized to enable the temperature rise to reach the minimum value. Therefore, the maximum value and the minimum value of electromagnetic force and temperature rise are required to be set, the signal-to-noise ratio of electromagnetic attraction force is set to be 52, and the signal-to-noise ratio of temperature rise is set to be 30, as shown in table 7.
TABLE 7 constraint values for SNR for factors and characteristic indices
Optimization is performed by using Design-expert11.0 software, and the obtained first group of combination level factor values are the optimization factor combinations. As shown in table 8, the number of combinations of hesitation factor values is large, and the present technical scheme only lists the first 9 groups.
Table 8 design combination of SNR optimization parameters for combining electromagnetic suction and temperature rise
As can be seen from Table 8, the inner diameter d of the armature 1 57.371mm; coil width l 1 38.096mm; spool height l 2 92.056mm; diameter d of enamelled wire 2 At 1.269mm, a maximum electromagnetic attraction signal-to-noise ratio and a minimum Wen Shengxin noise ratio are obtained.
According to nine groups of data obtained in the table 8, and in combination with JMAG simulation analysis, an electromagnetic attraction simulation analysis chart as shown in fig. 8 and a temperature rise simulation analysis chart as shown in fig. 9 are respectively obtained. Case1 to case9 in fig. 8 and 9 correspond to numbers 1 to 9 in table 8, respectively.
As can be seen from fig. 10 and 11, the inner diameter d of the armature 1 57.371mm; coil width l 1 38.096mm; spool height l 2 92.056mm; diameter d of enamelled wire 2 At 1.269mm, the maximum electromagnetic suction value and the minimum temperature rise value were obtained, thereby verifying the effectiveness and scientificity of the method.
The skilled person will know: although the present technical solution has been described according to the above specific embodiments, the inventive concept of the present technical solution is not limited to the present invention, and any modification applying the inventive concept of the present technical solution is included in the protection scope of the patent claims.
In the description of the present technical solution, it should be noted that the terms "center", "longitudinal", "transverse", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc. refer to the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, and are merely for convenience of describing the present technical solution and simplifying the description, and do not indicate or imply that the apparatus or element referred to must have a specific orientation, be configured and operated in a specific orientation, and thus should not be construed as limiting the present technical solution. Furthermore, the terms "first," "second," and the like, are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.
In the description of the present technical solution, it should be noted that, unless explicitly specified and limited otherwise, the terms "mounted," "connected," and "connected" are to be construed broadly, and may be, for example, fixedly connected, detachably connected, or integrally connected; can be mechanically or electrically connected; can be directly connected or indirectly connected through an intermediate medium, and can be communication between two elements. The specific meaning of the above terms in the present technical solution will be understood in specific cases by those skilled in the art. In addition, in the description of the present technical scheme, unless otherwise indicated, the meaning of "a plurality" is two or more.
The skilled person will know: although the present technical solution has been described according to the above specific embodiments, the inventive concept of the present technical solution is not limited to the present invention, and any modification applying the inventive concept of the present technical solution is included in the protection scope of the patent claims.
Claims (2)
1. The optimization design method for the multi-quality characteristic parameters of the electromagnet based on Taguchi and BBD is characterized by comprising the following steps:
A. selecting relevant design parameters, and designing and selecting a proper factor design level table by using a Taguchi method;
B. calculating the signal to noise ratio of electromagnetic attraction force and temperature rise in each group of combined tests in orthogonal tests provided by Box-Behnken (BBD) response surface analysis;
C. establishing a quadratic mathematical model between the BBD and each factor and verifying the validity of the model;
D. combining the maximum electromagnetic suction value and the minimum temperature rise value as optimization indexes to obtain the optimal quality characteristic parameter combination and carrying out experimental verification;
in the step A:
according to the self characteristics of the electromagnetic brake, determining two mutually related mass characteristics of maximum electromagnetic force and temperature rise of the electromagnetic brake as analysis objects, wherein the maximum electromagnetic force is a hopeful characteristic, and the temperature rise is a hopeful characteristic;
combining electromagnet parameter analysis, selecting the inner diameter of the iron pivot, the width of the coil, the height of the spool and the diameter of the enameled wire as controllable factors of a Taguchi orthogonal experiment;
calculating the level value of each influence factor according to the following three-level formulation formula:
wherein,、/>、/>three horizontal values representing controllable factors, respectively; />A central level value for each factor; />For each factor standard deviation, take +.>=0.1/>；
The step B comprises the following steps:
b1, correlating the two quality characteristics by using Taguchi and BBD analysis to obtain an optimal parameter design optimization combination;
b2, analyzing by adopting worst condition N1 and standard condition N2; obtaining the quality characteristic value in the orthogonal design combination analyzed by the BBD response surface through JMAG simulation and converting the quality characteristic value into a corresponding SNR value; the signal-to-noise ratio formula of the hope small characteristic is as follows:
(2) The signal-to-noise ratio formula of the telescopic characteristic is as follows:
(3) The signal-to-noise ratio formula of the eye observation characteristic is as follows:
wherein, thereinAnd->Standard deviation and mean values for the quality characteristics y; MSD is the mean square error of the quality characteristics;
the step C comprises the following steps:
c1, BBD response surface model selection,
B, designing and combining the step A according to a BBD orthogonal test method, and arranging a BBD response surface Design table by using Design-expert11.0 software;
under the general condition that P is smaller than 0.05, the model is obvious when P is smaller than 0.0.0, according to Design-expert11.0 software, the variance analysis of various models established based on the electromagnetic suction signal-to-noise ratio and the Wen Shengxin noise ratio is respectively carried out; selecting an effective and obvious high-order model of the additional item according to the BBD selection model as much as possible;
c2, BBD mathematical model establishment,
Fitting the relation between the quadratic function pair variable and the target variable according to a least square method by using Design-expert11.0 software to obtain a response function;
c3, BBD mathematical model response analysis,
The quadratic response mathematical model is established reliably according to the analysis of variance, which verifies that the quadratic model is significant.
2. The method for optimizing design of multiple quality characteristics parameters of an electromagnet based on Taguchi and BBD according to claim 1, wherein said step D comprises:
aiming at the electromagnetic suction force of the telescope index, when optimizing, all factors need to be optimized to maximize the electromagnetic suction force; the temperature rise belongs to the index of the hope subclass, and when optimizing, all factors are required to be optimized to enable the temperature rise to reach the minimum value; it is therefore necessary to set a maximum value where electromagnetic force cannot be achieved and a minimum value where temperature rise cannot be achieved.
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