JP2005251117A - Simulation method, design support apparatus, computer program and recording medium - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To run a simulation for the characteristic of a design object, in consideration of fluctuation of size or characteristic possessed by the design object or the component member of the design object, or manufacturing fluctuation or the like in the manufacturing process of the design object. <P>SOLUTION: The design object is approximated by a model having one or more parameters, a design value related to the design of the design object and a plurality of different values different from the design value are set, respectively for the one or more parameters, the design value and the plurality of different values are allocated to a plurality of levels, on the basis of an orthogonal table related to an experimental design, a plurality of characteristic values are calculated, an approximation expression related to the characteristic values of the model is derived from the plurality of calculated characteristic values, and on the basis of values of variables related to fluctuation from the design value that occurs in the manufacturing process, the characteristic values of the model are calculated by using the approximation expression. <P>COPYRIGHT: (C)2005,JPO&NCIPI

Description

  The present invention relates to a simulation method for calculating a characteristic value of a design object, for example, a cogging torque of a permanent magnet motor, using an analysis model, a design support apparatus, a computer program for causing a computer to calculate the characteristic value, and the computer program In particular, the present invention relates to a simulation method, a design support apparatus, a computer program, and a recording medium that calculate a characteristic value in consideration of the influence of variations in design values on characteristics of an analysis model.

  Conventionally, in the manufacture of a design object, a simulation method for approximating and calculating a characteristic value of the design object with an analysis model having a plurality of parameters is used. For example, in order to minimize the cogging torque of the permanent magnet motor, a method of simulating the cogging torque of the permanent magnet motor using a finite element method (FEM) is used (Patent Document 1, Patent Document 2). Cogging torque is uneven torque that occurs because the magnetic field potential generated by the magnet of a permanent magnet motor changes with respect to the rotation axis, and causes high-precision constant speed rotation, low vibration, and low noise. . When the simulation method is used, the characteristics of the design object can be estimated without actually manufacturing the design object, and the optimum shape, size, and material can be specified.

  However, even when the design object is actually manufactured based on the optimum parameter value specified by the simulation method, the desired characteristics are often not obtained depending on the design object. In other words, variations in the dimensions or characteristics of the design object or the constituent members of the design object during actual manufacture, or manufacturing variations in the manufacturing process of the design object greatly affect the characteristics of the design object. There is a problem that a design object having a desired characteristic value cannot be obtained.

  For example, even if the simulation is performed so that the cogging torque of the permanent magnet motor is 10 mN · m or less, the cogging torque value of the actually manufactured permanent magnet motor exceeds 100 mN · m. Variations sometimes occurred.

In response to this problem, a simulation method has been proposed in which the characteristic value of a design object is calculated in consideration of variations from the design value in the manufacturing process (Patent Document 3). The simulation method according to Patent Document 3 sets a plurality of levels, for example, three levels by an experimental design method, and assigns design values and variation values, for example, tolerances, related to variations from the design values to the three-level orthogonal table L _9. based on the orthogonal table L _9, a method of calculating the characteristics of the analytical model. According to this method, it is possible to estimate the characteristics of the design object when the design value fluctuates.
JP 2003-141183 A JP-A-8-101261 JP 2002-99579 A

  However, in order to obtain the desired characteristics in the method according to Patent Document 3, it is necessary to repeatedly change the fluctuation value and analyze the characteristic value again by the finite element method or the like. There was a problem.

  In addition, there is a problem that it is extremely inefficient because the analysis by the finite element method is repeated in the dark clouds without comparing the influence of the variation of each parameter value on the characteristics of the design object.

  The present invention has been made in view of such circumstances, and derives an approximate expression related to a characteristic value of a model, and uses the approximate expression to determine the dimensions of a design object or a component of the design object. Alternatively, even if variations from the design value occur in the manufacturing process by calculating the characteristic value of the design object taking into account the variation in characteristics or the manufacturing variation in the manufacturing process of the design object, A simulation method, a design support apparatus, a computer program for causing a computer to perform the calculation, and a record in which the computer program is recorded, which can specify design values and tolerances that allow a design object to secure desired characteristics The purpose is to provide a medium.

  In addition, by deriving an approximate expression based on the orthogonal table related to the design of experiment, a simulation method, a design support apparatus, and a computer that perform the calculation can reduce the statistical error of the characteristic value calculated by the approximate expression. It is another object of the present invention to provide a computer program to be executed and a recording medium in which the computer program is recorded.

  Furthermore, by repeatedly calculating the characteristic value until the calculated characteristic value falls within the desired characteristic range, it is possible to specify a design value and a variation value of the design object having the desired characteristic. It is another object of the present invention to provide a support device, a computer program for causing a computer to perform the identification, and a recording medium on which the computer program is recorded.

  Furthermore, when changing the variation value in order to obtain a desired characteristic, the design value and the variation value such that the design object has the desired characteristic by considering the influence of each parameter on the characteristic of the design object. It is another object of the present invention to provide a simulation method, a design support apparatus, a computer program for causing a computer to perform the specification, and a recording medium on which the computer program is recorded.

  Furthermore, by providing a permanent magnet motor as a design object to be simulated, a simulation method is provided that enables calculation of the characteristics of the permanent magnet motor in consideration of variations from design values in the manufacturing process. The purpose.

  Furthermore, the simulation method can calculate the characteristic value related to the cogging torque in consideration of the variation from the design value in the manufacturing process by setting the characteristic to be simulated to be related to the cogging torque of the permanent magnet motor. For other purposes.

  Furthermore, by setting values related to permanent magnets that have a large influence on cogging torque, such as dimensions and thickness, as parameters that take into account variations from design values in the manufacturing process, Another object is to provide a simulation method capable of estimating characteristics with higher accuracy.

  The simulation method according to the present invention approximates a design object with a model having one or a plurality of parameters, and a design value related to the design of the design object and a plurality of different values different from the design value for the one or more parameters. In a simulation method for setting a plurality of values and calculating a plurality of characteristic values of the model from the design values and / or the different values, an approximate expression related to the characteristic values of the model is derived based on the calculated characteristic values, A variation value related to variation from the design value of the design object is set, and a characteristic value of the model is calculated from the approximate expression and the variation value.

  The simulation method according to the present invention sets a plurality of levels according to an experiment design method, assigns the design value and / or the plurality of different values to the plurality of levels, and sets the plurality of characteristic values to the plurality of levels. It is calculated based on the orthogonal table concerning.

  The simulation method according to the present invention sets a characteristic range related to the design object, determines whether or not the characteristic value calculated by the approximate expression is within the characteristic range, and the characteristic value falls within the characteristic range. If it is determined that the characteristic value is not within the characteristic range, a variation value different from the variation value related to the characteristic value determined to be not within the characteristic range is set, and the characteristic value is further calculated using the set different variation value and the approximate expression. It is characterized by.

  The simulation method according to the present invention is characterized in that the plurality of characteristic values calculated based on the orthogonal table are subjected to an analysis of variance, and the different variation values are set based on a result of the analysis of variance.

  In the simulation method according to the present invention, the design object is a permanent magnet motor including a permanent magnet.

  In the simulation method according to the present invention, the characteristic value is a characteristic value related to a cogging torque of the permanent magnet motor.

  In the simulation method according to the present invention, the parameter is a parameter corresponding to a value related to a design of the permanent magnet.

  The design support apparatus according to the present invention is different from means for approximating a design object with a model having one or more parameters, a design value related to the design of the design object for the one or more parameters, and the design value. In a design support apparatus, comprising: a receiving unit that receives each of a plurality of different values; and a calculation unit that calculates a plurality of characteristic values of the model from the design values and / or the different values. Means for deriving an approximate expression related to the characteristic value of the model based on a value, and the accepting means comprises means for accepting a variation value related to a variation of the design object from the design value, and the calculating means Is characterized in that a characteristic value of the model is calculated from the approximate expression and the variation value.

  In the design support apparatus according to the present invention, the calculation means includes means for setting a plurality of levels according to an experiment design method, and means for assigning the design value and / or the plurality of different values to the plurality of levels. The plurality of characteristic values should be calculated based on an orthogonal table related to the plurality of levels.

  The design support apparatus according to the present invention includes means for accepting setting of a characteristic range relating to the design object, and determination means for determining whether or not the characteristic value calculated by the approximate expression is within the characteristic range. The calculation means, when the determination means determines that it is not within the characteristic range, an analysis of variance for analyzing the plurality of characteristic values calculated based on the orthogonal table, and an analysis of variance by the analysis of variance means And setting means for setting a fluctuation value that is different from the fluctuation value related to the characteristic value determined not to be within the characteristic range, and according to the different fluctuation values set by the setting means and the approximate expression. The characteristic value is further calculated.

  A computer program according to the present invention includes a step of causing a computer to approximate a design object with a model having one or a plurality of parameters, a computer having a design value related to the design of the design object with respect to the one or more parameters, and And / or a computer program having a step of calculating a plurality of characteristic values of the model from a plurality of different values different from the design value, the approximate expression relating to the characteristic value of the model based on the plurality of characteristic values calculated by the computer And a step of causing a computer to calculate a characteristic value of the model by a variation value related to a variation of the design object from the design value and the approximate expression.

  In the computer program according to the present invention, the step of calculating the plurality of characteristic values includes causing the computer to assign the design value and / or the plurality of different values to the plurality of levels related to the experiment design method, and And calculating the plurality of characteristic values on the basis of orthogonal tables according to the plurality of levels.

  The computer program according to the present invention includes a step of causing a computer to determine whether or not a characteristic value calculated by the approximate expression is within a characteristic range related to the design object; If it is determined that it is not within the characteristic range, the step of analyzing the plurality of characteristic values calculated based on the orthogonal table, and the computer is not within the characteristic range based on the result of the analysis of variance A step of setting a variation value different from the variation value related to the determined characteristic value; and a step of causing the computer to further calculate the characteristic value by using the set different variation value and the approximate expression. To do.

  The recording medium according to the present invention is a recording medium readable by a computer in which the computer program is recorded.

  In the first invention, the eighth invention, the eleventh invention, and the fourteenth invention, the size or characteristic of the design object that is actually scheduled to be manufactured, or the dimension or characteristic of the component of the design object. A plurality of characteristic values of the model are calculated from the corresponding design values and a plurality of different values different from the design values, and an approximate expression for approximately calculating the characteristic values from the calculated plurality of characteristic values is statistically derived. The approximate expression can approximately calculate the characteristic value of the model within the range of the design value and the different value. Based on a variation value from a design value, that is, a value related to a design object, a variation in dimensions or characteristics of a component of the design object, or a manufacturing variation in a manufacturing process of the design object, the approximation is performed. By calculating the characteristic value using the equation, it is possible to easily and quickly simulate the characteristic of the design object in consideration of the above-described various variations. For example, by setting certain design values and tolerances and simulating model characteristics, even if there are variations from the design values in the manufacturing process, the desired characteristics of the manufactured design object are secured. Such design values and tolerances can be specified in advance before manufacturing.

  In the second invention, the ninth invention, the twelfth invention, and the fourteenth invention, a statistical error is determined in order to set a level by an experimental design and estimate an approximate expression based on an orthogonal table related to the level. It is possible to derive an approximate expression having a small value. Therefore, a characteristic value with a small statistical error can be calculated by using the approximate expression.

  In the third invention, the tenth invention, the thirteenth invention, and the fourteenth invention, a characteristic range relating to a design object, for example, a characteristic that is set and calculated for a characteristic required for a design object that is actually manufactured. The variation value is changed and the approximate calculation is repeated until the value falls within the characteristic range. Therefore, it is possible to specify design values and variation values, for example, tolerances, of a design object that achieves desired characteristics. In addition, since the repeated characteristic value is calculated using the approximate expression, it is possible to specify the desired fluctuation value more quickly than in the case where the approximate expression is not used.

  In the fourth invention, the tenth invention, the thirteenth invention, and the fourteenth invention, an analysis of variance is performed using an orthogonal table, and a parameter for changing the variation value is determined based on the result of the analysis of variance. That is, the influence of each parameter variation on the characteristic value variation can be identified by analysis of variance. Therefore, it is possible to more efficiently specify a fluctuation value that falls within a desired characteristic range.

  In the fifth invention, since the design object is a permanent magnet motor, it is possible to calculate the characteristic value of the permanent magnet motor in consideration of variations in design values.

  In the sixth aspect of the invention, since the characteristic estimated using the approximate expression is a characteristic related to the cogging torque of the permanent magnet motor, the characteristic value related to the cogging torque of the permanent magnet motor is calculated in consideration of variations in design values. It becomes possible.

  In the seventh invention, since the parameter is a value related to the design of the permanent magnet that is considered to have a large influence on the fluctuation of the cogging torque compared to other parameters, the characteristics relating to the permanent magnet motor, such as the cogging torque, are further improved. It becomes possible to simulate accurately.

  In the first invention, the eighth invention, the eleventh invention, and the fourteenth invention, in consideration of the variation from the design value in the manufacturing process, the characteristic value of the design object is determined by an analysis means such as a finite element method. It becomes possible to calculate easily and quickly without repeated use, and it is possible to specify design values and tolerances necessary for manufacturing a design object having desired characteristics.

  In the second invention, the ninth invention, the twelfth invention, and the fourteenth invention, it is possible to calculate a characteristic value having a small statistical error.

  In the third invention, the tenth invention, the thirteenth invention, and the fourteenth invention, it is possible to easily and quickly specify the design value and the variation value of the design object having the desired characteristics.

  In the fourth invention, the tenth invention, the thirteenth invention, and the fourteenth invention, it is possible to efficiently specify a variation value that satisfies a desired characteristic.

  In the fifth invention, it is possible to calculate the characteristics of the permanent magnet motor in consideration of variations in the manufacturing process of the design value.

  In the sixth aspect of the invention, it is possible to calculate the characteristics relating to the cogging torque of the permanent magnet motor in consideration of variations in the manufacturing process.

  In the seventh invention, characteristics relating to the permanent magnet motor, such as cogging torque, can be more accurately simulated in consideration of variations in the manufacturing process.

  A simulation method according to the present invention will be described in detail with reference to the drawings showing embodiments thereof. FIG. 1 is a schematic cross-sectional view of a permanent magnet motor which is an example of a design object. FIG. 2 is a front view showing one of the permanent magnets provided in the permanent magnet motor. In FIG. 1, 1 is a cylindrical stator and has 27 teeth 1a inside. A coil (not shown) is attached to each of the teeth 1a. A rotor 2 is rotatably supported at the center of the stator 1. The rotor 2 includes a columnar rotor core 2a, and six permanent magnets 2b having an arc-shaped cross section are equally arranged and fixed on the outer circumferential surface of the rotor core 2a in the circumferential direction of the rotor core 2a.

  Hereinafter, a method for simulating cogging torque among the characteristics of the permanent magnet motor shown in FIG. 1 in consideration of variations in the manufacturing process will be described. First, in order to analyze the cogging torque of the permanent magnet motor by the finite element method, the permanent magnet motor is approximated by a model having a plurality of parameters such as the shape of the teeth 1a, the dimensions of the rotor core 2a, and the dimensions of the permanent magnet 2b.

  Next, a parameter value for minimizing the cogging torque, that is, a design value is specified by a known magnetic field analysis. Then, the specified design value is set for each of a plurality of parameters.

  Next, a parameter that is considered to be a factor affecting the cogging torque is extracted from the plurality of parameters. In the embodiment, the outer diameter R, the radial thickness Lm, the outer diameter chord width W, the inner diameter center-to-outer diameter width x, and the magnetic pole orientation direction of the permanent magnet 2b shown in FIG. The values Lθ, Lθx, and the value ε related to the displacement of the arrangement position of the permanent magnet 2b in the circumferential direction of the rotor core 2a shown in FIG. In general, it is considered that the size or characteristics of the permanent magnet 2b greatly affects the cogging torque.

  Next, the number of levels related to the experimental design method, for example, three levels is set, and as shown in Table 1 below, a design value and two different values different from the design value are assigned to each level for each parameter.

In Table 1, for example, a value Lm ₁ is assigned to level 1 of parameter Lm, a value Lm ₂ is assigned to level ₂ , and a value Lm ₃ is assigned to level 3. The values Lm _{1 to} Lm ₃ are the design value of the parameter Lm and two different values. The two different values may be set with reference to the production results of the permanent magnet motor. That is, it is only necessary to set parameter values that can change due to variations in design objects that occur in the manufacturing process in a well-balanced manner. Similarly, the parameters W, R, setting x, Lθ, Lθx, the value in level i of epsilon each _{W i, R i, x i} , Lθ i, Lθx i, ε i the (i = 1, 2, 3) To do.

Next, parameters and levels are assigned to the orthogonal table L ₂₇ shown in Table 2.

Then, based on the orthogonal table L ₂₇ , the cogging torque values T _{1 to} T ₂₇ of each model, that is, No. _{1 to No. 27} are calculated by the finite element method. For example, in the case of model No. 1, values of level 1 are set for the parameters Lm, W, R, x, Lθ, Lθx, and ε, and the cogging torque value T ₁ is calculated by the finite element method.

Next, using the 27 cogging torque values T _{1 to} T ₂₇ calculated for each model as samples, an approximate expression of the cogging torque relating to a plurality of parameters is derived. In the present embodiment, since the interaction of each parameter is small, a first-order approximate expression is assumed for each parameter without considering the interaction. The approximate expression is represented by the following expression.

Here, β _{0 to} β ₇ are partial regression coefficients. Next, the value of the partial regression coefficient β _i (i = 0 to 7) is estimated by performing multiple regression analysis of Formula 1 using the characteristic values T _{1 to} T ₂₇ calculated based on the orthogonal table as samples.

  Next, a variation value of the parameter, that is, a value related to the variation of the design object generated in the manufacturing process, for example, an appropriate tolerance is set, and the value of the cogging torque when the design value of the parameter has the tolerance, Calculation is performed using the derived approximate expression. Therefore, the variation range of the cogging torque value can be estimated from the design value of the permanent magnet motor and the tolerance of the design value. Here, since the purpose is to suppress the value of the cogging torque to a predetermined value or less, it is sufficient to calculate the maximum value Tmax of the cogging torque.

  Next, a characteristic range related to the permanent magnet motor, that is, an allowable cogging torque allowable maximum value Tp is set, and it is determined whether or not the cogging torque of the permanent magnet motor having a design value and tolerance is within the characteristic range. . That is, it is determined whether or not the maximum value Tmax of the cogging torque is equal to or less than the allowable maximum value Tp.

When it is determined that the maximum value Tmax exceeds the allowable maximum value Tp, the variation value such as the tolerance is repeatedly changed until the calculated maximum value Tmax of the cogging torque becomes equal to or less than the allowable maximum value Tp, and the value of the cogging torque Is calculated. Here, selection of a parameter for changing the variation value will be described. When changing the fluctuation value, the cogging torque can be minimized more effectively when the tolerance of a parameter having a large influence on the fluctuation of the cogging torque among the plurality of parameters is changed. Therefore, based on the orthogonal table L _27, and analysis of variance for each parameter, examine the effect of changes in the value of each parameter has on the change in the value of the cogging torque. FIG. 3 is a graph showing the value of the cogging torque with respect to the level of each parameter. The horizontal axis represents the level of each parameter, and the vertical axis represents the average value of cogging torque at each level. Therefore, it can be estimated that a parameter having a large change in cogging torque value with respect to a change in level has a large variance and a large influence of the fluctuation value on the cogging torque. For example, it can be estimated from FIG. 3 that the influence of fluctuations in parameters ε, W, and x on fluctuations in cogging torque is large. Therefore, it is preferable to repeatedly calculate the cogging torque value by changing the variation values of the parameters ε, W, and x.

  FIG. 4 is a block diagram schematically showing a design support apparatus according to the present invention. The design support apparatus is, for example, a personal computer or a workstation. In FIG. 4, reference numeral 30 denotes a control unit composed of a CPU, which is connected to the bus 31. Connected to the bus 31 are a ROM 32 storing a control program necessary for the control unit 30 to control various hardware described later, and a RAM 33 for temporary storage. A storage unit 34, for example, a hard disk, connected to the bus 31 stores a computer program according to the present invention. The control unit 30 activates the computer program and develops a predetermined program part in the RAM 33. And it operates as a design support apparatus by executing processing related to a computer program.

  In FIG. 4, reference numeral 35 denotes an input unit composed of a keyboard, a mouse, and the like, which inputs parameter values for specifying a design object, operation instructions for the design support apparatus, and the like. The display unit 36 is a CRT or a liquid crystal display that displays the processing result of the control unit 30. The reading unit 37 is a disk drive that reads the computer program from the recording medium 4 such as a CD-ROM or DVD that records the computer program according to the present invention. The computer program read from the reading unit 37 is stored in the storage unit 34.

  A processing procedure executed by the design support apparatus according to the present invention will be specifically described. FIG. 5 is a flowchart showing the processing procedure of the design support apparatus according to the present invention. First, the control unit 30 performs a process of approximating the design object with a model having one or a plurality of parameters (step S1). Here, a model for analyzing the permanent magnet motor shown in FIG. 1 by the finite element method is generated.

  Next, the control unit 30 receives the design value of the permanent magnet motor and two different values different from the design value via the input unit 35, and assigns the received design value and each of the two different values to the three levels (steps). S2). Table 3 below shows the design values and the two different values assigned to each level.

  As shown in Table 3, the design value 3.0 is assigned to the parameter Lm to the level 2, and the different values 2.9 and 3.1 are assigned to the level 1 and the level 3, respectively. In Table 3, the values displayed on the hatched cells are design values, and the values displayed on the white cells are different values. Similarly, design values and different values are assigned to the parameters W, R, x, ε, Lθ, and Lθx, respectively.

Next, based on the orthogonal table L ₂₇ shown in Table 2, the control unit 30 calculates the cogging torque values T _{1 to} T ₂₇ of the models No 1 to No ₂₇ by the finite element method (step S3). Then, based on the calculated cogging torque values T _{1 to} T ₂₇ , approximate equations for the cogging torque for the eight parameters are derived (step S4). Table 4 below shows partial regression coefficients β _{0 to} β ₇ estimated when Equation 1 is assumed as an approximate expression.

  Next, the setting of the desired characteristic range of the design object is accepted (step S5). In order to minimize the cogging torque, an allowable maximum value Tp of the cogging torque, that is, an allowable maximum value of the cogging torque, for example, 9 mN · m is received. And the setting of the tolerance of a design value is received (step S6). For example, input of set values and tolerances as shown in Table 5 below is accepted.

  Next, a cogging torque value, particularly a maximum value Tmax, when there is a tolerance is calculated (step S7). When the design value and tolerance shown in Table 5 are set, the maximum value Tmax is calculated as 9.19 mN · m. Then, it is determined whether or not the maximum value Tmax is equal to or less than the allowable maximum value Tp (step S8). If it is determined that the maximum value Tmax is less than or equal to the allowable maximum value Tp (step S8: YES), the process is terminated. If the maximum value Tmax is greater than or equal to the allowable maximum value Tp (step S8: NO), the process returns to step S6. For example, when the allowable maximum value Tp is 9 mN · m, Tmax = 9.19 is equal to or greater than the allowable maximum value Tp, so the control unit 30 returns the process to step S6 and accepts the tolerance setting again.

  Here, among the tolerances shown in Table 5, the user of the design support apparatus may reset the tolerances of the parameters W and ε that are considered to be factors that increase the cogging torque from FIG. For example, when the tolerance of the parameter W is set to ± 0.05 and the tolerance of the parameter ε is set to + 0.1 / −0, the control unit 30 sets the maximum cogging torque value Tmax to 6.86 mN · in step S7. m is calculated, and it is determined in step S8 that the allowable maximum value Tp is equal to or less than 9 mN · m (step S8: YES).

  Accordingly, in Step 8, by designing and manufacturing the permanent magnet motor based on the design value and tolerance when it is determined that the allowable maximum value Tp or less, variation in the dimensions or characteristics of the parts constituting the permanent magnet motor, Or even if it is a case where the dispersion | variation in a manufacturing process arises, the permanent magnet motor which can ensure a desired characteristic can be manufactured efficiently, and manufacturing cost can be reduced.

  According to the simulation method, the design support apparatus, the computer program, and the recording medium according to the present invention, it is possible to simulate the characteristics of the design object in consideration of variations in the size or shape of the design object in the manufacturing process. That is, it is possible to estimate the variation in cogging torque of a permanent magnet motor that is actually manufactured. Therefore, it is possible to specify design values and tolerances necessary for manufacturing a permanent magnet motor having desired characteristics.

  Also, when changing the tolerance to obtain the desired characteristics, the parameters W, ε, and x are selected as factors that increase the cogging torque, so it is more efficient than changing the tolerance to the dark clouds. It becomes possible to specify design values and tolerances of a permanent magnet motor having desired characteristics.

  In addition, because it is a parameter that fluctuates the size of the permanent magnet, which is considered to have a significant effect on the value of the cogging torque, it is possible to estimate the characteristics of the cogging torque that is actually manufactured more accurately and to set tolerances. It becomes possible to carry out appropriately.

  In the present embodiment, the characteristic value is calculated using a first-order approximation formula for each parameter. However, the present invention is not limited to this, and a second-order approximation represented by the following formula is used. An expression may be used.

Here, n is the number of parameters, β _i and β _jk (i = 0 to n, j, k = 1 to n) are partial regression coefficients, and x _i (i = 1 to n) are parameters. In particular, an approximate expression represented by the following expression may be assumed in consideration of a second-order interaction regarding each parameter and a part of the interaction.

The partial regression coefficients β _i and β _{jk in} Equation 3 can be estimated by multiple regression analysis. According to the approximate expression derived by the multiple regression analysis, the maximum value of the cogging torque is calculated as 10.60 mN · m from the design values and tolerances shown in Table 5. Further, when the tolerances of the parameters W and ε are changed as shown in the embodiment, the maximum value of the cogging torque is calculated as 6.81 mN · m.

  FIG. 6 is a graph showing a correlation between a calculated value of cogging torque and an estimated value based on an approximate expression. The correlation coefficient according to Equation 1 is 0.57, and the correlation coefficient according to Equation 3 is 0.97. Therefore, compared with the approximate expression of Expression 1, the approximate expression of Expression 3 has much higher estimation accuracy, and it is possible to estimate the characteristics related to the cogging torque of the permanent magnet motor more accurately and perform an accurate design. Become.

  On the other hand, even the approximate expression of Equation 1 has a relatively high correlation coefficient of 0.57, so that the cogging torque value can be estimated with appropriate accuracy. Actually, as described above, the value of the cogging torque calculated by Expression 1 is close to the value calculated by Expression 3. Therefore, when simulating, it is only necessary to compare the accuracy required for the design and the simulation time and select an appropriate approximate expression.

  On the other hand, in this embodiment, the cogging torque is simulated, but the present invention is not limited to this, and other characteristics of the permanent magnet motor may be simulated.

  Further, although the characteristics of the permanent magnet motor are calculated, the present invention is not limited to this, and other design objects may be used.

  Furthermore, although the absolute value of cogging torque is calculated, the present invention is not limited to this, and it calculates torque that is a vector amount, pressure acting on a stator or rotor of a permanent magnet motor, stress that is a tensor amount, and the like. There may be. In this case, it is preferable to derive the approximate expression by performing multivariate multiple regression analysis on the partial regression coefficient of the approximate expression and estimating it.

  Furthermore, although the approximate expression is derived based on the orthogonal table related to the experimental design method, the present invention is not limited to this, and design values and different values are assigned uniformly and approximated using a plurality of derived characteristic values. An expression may be derived.

  Furthermore, the design value and / or different value means the design value and different value and the design value or different value. Therefore, calculating a plurality of model characteristic values from design values and / or different values means calculating characteristic values from design values and different values, calculating characteristic values from different values, and calculating characteristic values from design values. Means each.

It is a schematic sectional drawing of the permanent magnet motor which is an example of a design target object. It is a front view which shows one of the permanent magnets with which a permanent magnet motor is provided. It is a graph which shows the value of the cogging torque with respect to the level of each parameter. It is the block diagram which showed typically the design support apparatus which concerns on this invention. It is the flowchart which showed the process sequence of the design support apparatus which concerns on this invention. It is the graph which showed the correlation with the calculated value of cogging torque, and the estimated value by an approximate expression.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Stator 1a Teeth 2 Rotor 2a Rotor core 2b Permanent magnet 4 Recording medium 30 Control part 31 Bus 32 ROM
33 RAM
34 storage unit 35 input unit 36 display unit 37 reading unit

Claims (14)

The design object is approximated by a model having one or a plurality of parameters, a design value related to the design of the design object and a plurality of different values different from the design value are set in the one or a plurality of parameters, and the design In a simulation method for calculating a plurality of characteristic values of the model from values and / or the different values,
Deriving an approximate expression related to the characteristic value of the model based on the calculated characteristic values,
Set a variation value related to variation from the design value of the design object,
A characteristic value of the model is calculated from the approximate expression and the variation value. Set multiple levels for the design of experiments,
Assigning the design value and / or the plurality of different values to the plurality of levels,
The simulation method according to claim 1, wherein the plurality of characteristic values are calculated based on an orthogonal table according to the plurality of levels. Set a characteristic range related to the design object,
Determine whether the characteristic value calculated by the approximate expression is within the characteristic range;
When it is determined that the characteristic value is not within the characteristic range, a variation value different from the variation value related to the characteristic value determined not to be within the characteristic range is set,
The simulation method according to claim 1, wherein the characteristic value is further calculated by using different set fluctuation values and the approximate expression. Analyzing the plurality of characteristic values calculated based on the orthogonal table;
The simulation method according to claim 3, wherein the different variation values are set based on a result of analysis of variance. The design object is
It is a permanent magnet motor provided with a permanent magnet, The simulation method as described in any one of Claims 1 thru | or 4. The characteristic value is
The simulation method according to claim 5, wherein the simulation value is a characteristic value related to cogging torque of the permanent magnet motor. The parameter is
The simulation method according to claim 5, wherein the parameter corresponds to a value related to a design of the permanent magnet. Means for approximating the design object with a model having one or a plurality of parameters; and accepting means for receiving a design value relating to the design of the design object for the one or more parameters and a plurality of different values different from the design value And a design support device comprising a calculation means for calculating a plurality of characteristic values of the model from the design value and / or the different value,
The calculating means includes
Means for deriving an approximate expression related to the characteristic value of the model based on the plurality of calculated characteristic values;
The accepting means is
Means for receiving a variation value related to variation from the design value of the design object;
The calculating means includes
The design support apparatus is characterized in that a characteristic value of the model is calculated from the approximate expression and the variation value. The calculating means includes
Means for setting a plurality of levels related to the design of experiments;
Means for assigning the design value and / or the plurality of different values to the plurality of levels,
The design support apparatus according to claim 8, wherein the plurality of characteristic values are calculated based on an orthogonal table related to the plurality of levels. Means for accepting setting of a characteristic range relating to the design object;
Determination means for determining whether or not the characteristic value calculated by the approximate expression is within the characteristic range; and
The calculating means includes
If the determination means determines that it is not within the characteristic range, an analysis of variance means for analyzing the variance of the plurality of characteristic values calculated based on the orthogonal table;
Setting means for setting a variation value different from the variation value related to the characteristic value determined not to be within the characteristic range based on the result of the analysis of variance by the analysis of variance means;
The design support apparatus according to claim 9, wherein the characteristic value is further calculated based on different variation values set by the setting unit and the approximate expression. A step of causing a computer to approximate a design object with a model having one or more parameters; and a computer having a design value related to the design of the design object with respect to the one or more parameters and / or a plurality of different design values. And calculating a plurality of characteristic values of the model from different values of
Causing the computer to derive an approximate expression related to the characteristic value of the model based on the calculated plurality of characteristic values;
A computer program comprising: causing a computer to calculate a characteristic value of the model based on a variation value related to a variation of the design object from the design value and the approximate expression. The step of calculating the plurality of characteristic values includes:
Causing the computer to assign the design value and / or the plurality of different values to a plurality of levels according to an experiment design method;
The computer program according to claim 11, further comprising: causing the computer to calculate the plurality of characteristic values based on orthogonal tables according to the plurality of levels. Causing the computer to determine whether or not the characteristic value calculated by the approximate expression is within a characteristic range related to the design object;
When the computer determines that the characteristic value is not within the characteristic range, a step of performing an analysis of variance of the plurality of characteristic values calculated based on the orthogonal table;
A step of causing a computer to set a variation value different from the variation value related to the characteristic value determined not to be within the characteristic range based on the result of analysis of variance;
The computer program according to claim 12, further comprising: causing the computer to further calculate the characteristic value by using different set variation values and the approximate expression. 14. A recording medium readable by a computer on which the computer program according to claim 11 is recorded.

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