JP4554426B2 - Simulation model creation method and program, and recording medium recording program - Google Patents

Description

  The present invention models a part constituting a product as a system element and creates a product model from the system element, thereby reproducing a product entity on a computer, and a simulation model creation program, The present invention also relates to a computer-readable storage medium that records a simulation model creation program.

  In recent years, for the purpose of shortening product development, it has become common to perform evaluation and confirmation of performance and functions, which were conventionally performed by actual tests using prototypes, at the initial stage of development by simulation. Yes. In a product, a plurality of unitized parts are usually connected to each other, and the functions are intertwined. In modeling such a complex system on a computer, each part of the product is It is important to organize the physical state quantity to be transferred and to structure the model that can handle each part independently. And it is necessary to couple | bond between each component, without the change of energy producing.

  As a method for realizing this, conventionally, for example, Japanese Patent Application Laid-Open No. 09-91334 discloses a model (hereinafter referred to as a model) corresponding to each component constituting an entity by connecting energy flows with the concept of energy potential components and flow components. (Referred to as a component model) is expressed by a system equation. An example in which component models having a one-to-one relationship are combined using this concept will be described.

  FIG. 10 shows a one-to-one relationship between a potential difference component of energy applied to an entity as a state quantity and an input / output state quantity pair consisting of a flow quantity representing a flow component as a state quantity. It is a figure which shows the component model connected mutually. Regarding the modeling of electrical system functional parts, among the state quantities that combine the parts models, the state quantity expressed along Kirchhoff's voltage law is the level difference (here, voltage), while it follows the Kirchhoff current law. The amount of state expressed by the equation is a flow amount (here, current), and the difference amount Pao output from the component model A (“component A” in the figure) between the component models shown in FIG. The flow amount Fbo output from the component model B is combined with the flow amount Fai input to the component model A. ing. When the component models A and B are combined, the output of the component model of the connection source is substituted into the input of the component model that is the connection destination based on the conditions of Pao = Pbi and Fbo = Fai.

（数式２）

Ｘａドットは部品モデルＡに関する状態変数，Ａａ，Ｂａ，Ｃａは係数行列である。また、同様に、Ｘｂドットは部品モデルＢに関する状態変数，Ａｂ，Ｂｂ，Ｃｂは係数行列である。なお、ここでは、説明を簡単化するために、部品モデルを全て線形システムで表現するため、伝達係数Ｄｘは全て０となる。 In this case, the component models A and B can be expressed by the following system equations, respectively. In this system equation, the parameters of the internal characteristics of the model to which input / output state quantities are added are arranged in a matrix form with rows as output state vectors and columns as input state vectors. This constitutes the matrix.
(Formula 1)

(Formula 2)

Xa dots are state variables related to the component model A, and Aa, Ba, and Ca are coefficient matrices. Similarly, Xb dots are state variables related to the component model B, and Ab, Bb, and Cb are coefficient matrices. Here, in order to simplify the explanation, all the component models are expressed by a linear system, so that the transfer coefficients Dx are all zero.

First, the following equations are obtained by combining the system equations of the component models A and B such that the coefficient matrices are arranged in the diagonal component direction.
(Formula 3)

From here, by executing the substitution process of Pbi = Pao, the Pbi column can be deleted, and the following equation is obtained.
(Formula 4)

上記数式５を並べ替えることで、次式が得られる。
（数式６）

Next, by executing the substitution process of Fai = Fbo, the Fai column can be deleted, and the following expression is obtained.
(Formula 5)

By rearranging Equation 5 above, the following equation is obtained.
(Formula 6)

Finally, by deleting the output that is no longer necessary, the following equation is obtained as a system equation representing a model after the combination of the component models A and B having a one-to-one relationship.
(Formula 7)

  By the way, in practice, in many cases, three or more part models function in a complicated manner rather than when the part models function in a one-to-one relationship. When the above functional parts are modeled, it is common that the above-described coupling is performed so that they fit in a one-to-one relationship. For example, when modeling a vehicle body and four tires, the four tires are treated as one virtual model, and the models corresponding to the vehicle body and the tires are combined so as to match the number of pairs. In other words, when there are three or more part models that are related to each other, since a plurality of part models cannot be handled separately, for example, modeling considering only a part of the four wheels (for example, two wheels), etc. It was impossible to model appropriately for various needs.

  As a means for solving such a problem, Japanese Patent Application Laid-Open No. 2002-175338 discloses a method in which a plurality of functional parts are separately modeled, and a connection between three or more part models having a one-to-many relationship is connected to the energy described above. A method has been suggested that uses the concept of potential component and flow component.

JP 09-91334 A JP 2002-175338 A

  However, Japanese Patent Laid-Open No. 2002-175338 suggests a connection between component models having a one-to-many relationship using the concept of energy potential component and flow component, but a specific example for achieving this is shown. There is no disclosure about the calculation process. Further, the calculation processing for achieving the connection between the component models having the one-to-many relationship can be executed more easily and efficiently in order to facilitate the program development and increase the processing speed. desired.

  The present invention has been made in view of the above technical problems, and can simulate individual component models constituting a real model, and can easily and efficiently combine component models. It is an object to provide a model creation method, a simulation model creation method, a simulation model creation program, and a recording medium on which the simulation model creation program is recorded.

Accordingly, the first invention combines part models corresponding to a plurality of parts set independently for each predetermined function as elements constituting an entity to be simulated, and creates an entity model corresponding to the entity. A simulation model creation method, wherein a potential difference of energy applied to each of the above components and a flow amount as a state quantity representing a flow component and a flow quantity as a state quantity representing a flow component are paired with the input / output state quantity. A system that configures an internal matrix corresponding to the above-described difference amount and flow amount by arranging internal characteristic parameters of components to which state quantities are added in a matrix form in which rows are output state vectors and columns are input state vectors. In the simulation model creation method that expresses each of the above part models with an equation,
While applying at least three or more component models to a one-to-many relationship in which a plurality of submodels are connected in parallel to one reference model, the following relational expression U _criterion = Y ₁ + Y ₂ +. + Y _N-1
Y _reference = U ₁ = U ₂ =... = U _N-1
U _standard : input state quantity of the standard model
Y _standard : Output state quantity of the standard model
U ₁ , U ₂ ,..., U _N-1 : Input state quantity of each sub model
Y ₁ , Y ₂ ,..., Y _N-1 : Output state quantity of each sub model
N: based on the total number of component models, a step of interconnecting the input / output state quantity pairs, and a step of combining the system equations of the sub models.
In the system equation after combination, based on the relational expression of the input / output state quantity, a step of adding a row and a column and configuring a system equation of one composite model corresponding to a plurality of submodels;
Combining the system equation of the composite model with the system equation of the reference model;
In the system equation in which the system equation of the composite model is combined with the system equation of the reference model, the following relational expression U _standard = Y _composite
Y _standard = U _compound
U _compound : input state quantity of compound model
Y _compound : a step of performing substitution processing between input and output based on the output state quantity of the compound model;
A step of deleting unnecessary columns for each of the substitution processes.

Further, the second invention combines part models corresponding to a plurality of parts set independently for each predetermined function as elements constituting an entity to be simulated, and creates an entity model corresponding to the entity. A simulation model creation method, wherein a potential difference of energy applied to each of the above components and a flow amount as a state quantity representing a flow component and a flow quantity as a state quantity representing a flow component are paired with the input / output state quantity. A system that configures an internal matrix corresponding to the above-described difference amount and flow amount by arranging internal characteristic parameters of components to which state quantities are added in a matrix form in which rows are output state vectors and columns are input state vectors. In the simulation model creation method that expresses each of the above part models with an equation,
While applying at least three or more component models to a one-to-many relationship in which a plurality of submodels are connected in parallel to one reference model, the following relational expression U _criterion = Y ₁ + Y ₂ +. + Y _N-1
Y _reference = U ₁ = U ₂ =... = U _N-1
U _standard : input state quantity of the standard model
Y _standard : Output state quantity of the standard model
U ₁ , U ₂ ,..., U _N-1 : Input state quantity of each sub model
Y ₁ , Y ₂ ,..., Y _N-1 : Output state quantity of each sub model
N: based on the total number of part models, the step of interconnecting with the above pair of input / output state quantities;
Combining the system equations for all part models,
In the system equation after the combination, a step of performing substitution processing between input and output based on the relational expression of the input and output state quantity;
And a step of deleting unnecessary rows and columns after all the substitution processes.

Furthermore, the third invention combines part models corresponding to a plurality of parts set independently for each predetermined function as an element constituting an entity to be simulated, and creates an entity model corresponding to the entity. A simulation model creation device, wherein a potential amount of energy applied to each of the components is a state quantity representing a potential component and a flow quantity representing a flow component is a pair of input / output state quantities, and the input / output A system that configures an internal matrix corresponding to the above-described difference amount and flow amount by arranging internal characteristic parameters of components to which state quantities are added in a matrix form in which rows are output state vectors and columns are input state vectors. In the simulation model creation device that expresses each part model with the equation,
While applying at least three or more component models to a one-to-many relationship in which a plurality of submodels are connected in parallel to one reference model, the following relational expression U _criterion = Y ₁ + Y ₂ +. + Y _N-1
Y _reference = U ₁ = U ₂ =... = U _N-1
U _standard : input state quantity of the standard model
Y _standard : Output state quantity of the standard model
U ₁ , U ₂ ,..., U _N-1 : Input state quantity of each sub model
Y ₁ , Y ₂ ,..., Y _N-1 : Output state quantity of each sub model
N: based on the total number of part models, a procedure for interconnecting with the above pair of input / output state quantities;
Combining the system equations of each of the above submodels;
In the system equation after the combination, on the basis of the relational expression of the input / output state quantity, a procedure for constructing a system equation of one composite model corresponding to a plurality of submodels by adding and coupling rows and columns;
Combining the system equation of the composite model with the system equation of the reference model;
In the system equation in which the system equation of the composite model is combined with the system equation of the reference model, the following relational expression U _standard = Y _composite
Y _standard = U _compound
U _compound : input state quantity of compound model
Y _composite : A procedure for performing substitution processing between input and output based on the output state quantity of the composite model;
This is a simulation model creation program for executing a procedure for deleting unnecessary columns for each substitution process.

Furthermore, the fourth invention combines a part model corresponding to a plurality of parts set independently for each predetermined function as an element constituting an entity to be simulated, and an entity model corresponding to the entity is obtained. A simulation model creation apparatus for creating a pair of input / output state quantities, wherein a potential difference amount representing a potential component of energy applied to each component and a flow amount serving as a state quantity representing a flow component are paired with an input / output state quantity, The internal characteristic parameters of the parts to which the input / output state quantity is added are arranged in a matrix format in which the row is the output state vector and the column is the input state vector. In the simulation model creation device that expresses each part model with the system equation to
While applying at least three or more component models to a one-to-many relationship in which a plurality of submodels are connected in parallel to one reference model, the following relational expression U _criterion = Y ₁ + Y ₂ +. + Y _N-1
Y _reference = U ₁ = U ₂ =... = U _N-1
U _standard : input state quantity of the standard model
Y _standard : Output state quantity of the standard model
U ₁ , U ₂ ,..., U _N-1 : Input state quantity of each sub model
Y ₁ , Y ₂ ,..., Y _N-1 : Output state quantity of each sub model
N: based on the total number of part models, a procedure for interconnecting with the above pair of input / output state quantities;
The procedure to combine the system equations of all part models,
In the system equation after the combination, based on the relational expression of the input / output state quantity, a procedure for performing substitution processing between input and output,
This is a simulation model creation program that executes a procedure for deleting unnecessary rows and columns after all substitution processes.

Furthermore, the fifth invention is a recording medium on which a simulation model creation program according to the third invention is recorded.

Furthermore, the sixth invention is a recording medium on which the simulation model creation program according to the fourth invention is recorded.

According to the first invention of the present application, when a plurality of component models having a one-to-many relationship are combined, a plurality of rows and columns are added and combined when the component models corresponding to many are combined into one in advance. In addition, the total number of rows and columns can be reduced, the subsequent calculation processing can be executed more easily and efficiently, and high-speed calculation processing can be expected.

Further, according to the second invention of the present application, when combining a plurality of component models having a one-to-many relationship, combining all the component models and repeating the basic combining process, an unnecessary matrix is generated. By deleting, as a result, a plurality of component models can be combined, and program development and calculation processing can be speeded up.

Furthermore, according to the third invention of the present application, the same effect as that of the first invention can be obtained.

Furthermore, according to the fourth invention of the present application, the same effect as that of the second invention can be obtained.

Furthermore, according to the fifth invention of the present application, the same effect as that of the first invention can be obtained.

Furthermore, according to the sixth invention of the present application, the same effect as that of the second invention can be obtained.

Embodiments of the present invention will be described below with reference to the accompanying drawings.
FIG. 1 is a diagram illustrating a hardware configuration of a simulation model creation apparatus (hereinafter referred to as a model creation apparatus) according to an embodiment of the present invention. The model creation apparatus 10 creates an actual simulation model and executes a simulation using the model. As a basic configuration, the model creation apparatus 10 manages the execution of an application program and exchanges data with each peripheral device. A CPU 1 that performs sequence control of the apparatus main body based on an operating system (hereinafter referred to as OS) that is a basic software that provides functions, a ROM 2 that records a program executed when the model creation apparatus 10 is started, and various programs RAM 3 used as a buffer area of a work area necessary for execution of the program, and a hard disk (“HD” in the figure) 4 for storing the OS, application programs, and various data.

  The model creation apparatus 10 also visually displays an interface unit (“I / F” in the figure) 5 for transmitting / receiving data to / from various external devices and various information such as application screens. A display unit 6 as a possible monitor display, an input unit 7 such as a keyboard and a mouse for a user to input various settings, and an optical disc drive 8 for reading and writing data on an optical disc such as a CD or a DVD. is doing. Further, although not particularly illustrated, the model creating apparatus 10 may have other configurations such as a floppy (registered trademark) disk drive. As the model creation device 10, a general-purpose personal computer can be used.

  A simulation program for executing the above simulation is stored in the hard disk 4 of the model creating apparatus 10, and is read and executed as necessary. The simulation program is stored in the hard disk 4 of the model creating apparatus 10 by using an external recording medium such as an optical disk such as a DVD or a CD or a floppy (registered trademark) disk or via a network.

  FIG. 2 is an explanatory diagram showing a rough flow of a simulation including the execution of a vehicle traveling simulation using the model from the creation of a vehicle model corresponding to the entire vehicle, taking the vehicle traveling simulation as an example. In this simulation, the vehicle running simulation using the vehicle model is not limited to execution, and the results measured in the actual vehicle running test are analyzed based on the simulation program and compared with the results of the vehicle running simulation using the vehicle model. Can be done.

  In this simulation, first, a model corresponding to a vehicle as a simulation target composed of a plurality of functional parts is created (# 11). The vehicle model is created by modeling various parts constituting the vehicle as system elements and combining models corresponding to the parts (hereinafter referred to as part models). Details of model creation will be described later.

  After that, for the created vehicle model, parameters related to the parts that make up the vehicle (such as vehicle body running resistance and tire loss resistance), and the same conditions as the actual vehicle running test (eg road slope, temperature, pressure, etc.) ) And data corresponding to the same driving operation as the actual vehicle running test are input (# 12, # 13 and # 14), and a vehicle running simulation is executed (# 15).

  When various parameters relating to vehicle travel are measured in the actual vehicle travel test (# 16), the measurement results are analyzed (# 17) and compared with the simulation results obtained in # 15. Thereby, the vehicle model created in # 11 is evaluated. Data representing the vehicle running simulation result in # 15 and the analysis and evaluation results in # 17 are output to a display, a plotter, etc. according to a preset format, and recorded in a storage device such as the hard disk 4 (# 18).

  FIG. 3 is a flowchart of the simulation executed by the model creation apparatus 10 based on the simulation program stored in the ROM 2. In this simulation, first, it is determined whether or not a plurality of component models have been selected as elements constituting the entity model (S21). This selection can be arbitrarily performed by the user. As a result, when it is determined that the part model is not selected, step S21 is repeated. On the other hand, when it is determined that the part model is selected, the energy is subsequently transferred between the selected part models. A connection that does not change is set (S22). Thus, a plurality of component models are connected to each other by a pair of input / output state quantities while being applied to a one-to-one relationship or a one-to-many relationship. When three or more part models are selected, a plurality of other part models are connected in parallel to one part model in order to apply the plurality of part models to a one-to-many relationship. It is assumed that

  Thereafter, a plurality of component models are combined (S23), and a system equation of a real model to be simulated is derived. Subsequently, initial values of parameters and state quantities (input / output variables and state variables) are set (S24), and simulation of the combined real model is executed (S25), corresponding to the real model to be simulated. The system equation of the combined model is calculated.

  Next, it is determined whether or not there has been a request to end the simulation execution (S26). As a result, if it is determined that there is no request, the process returns to step S25, and the subsequent steps are repeated. If it is determined that there is a simulation result, a simulation result is output (S27). As described above, the simulation is executed based on the simulation program stored in the ROM 2.

  In this embodiment, in particular, a plurality of (particularly three or more) component models are further added in the component model combination process (S23 in the flow of FIG. 3) for deriving the system equation of the real model to be simulated. A device has been devised for easy and efficient coupling. In the following, specifically, three part models A, B, and C are selected as elements constituting the real model, and these models are referred to as part models B and C connected in parallel to part model A. An example will be described in which a real model is combined after being connected to each other by a pair of input / output state quantities while being applied to a one-to-two relationship.

  FIG. 4 shows component models A, B, and C that are connected to each other by a pair of input / output state quantities (a “component A” in FIG. , “Part B” and “Part C”). As in the case described with reference to FIG. 10, among the state quantities that combine the component models, the state quantity expressed along Kirchhoff's voltage law is the amount of difference in the modeling of the electrical functional parts. On the other hand, the state quantity expressed in accordance with Kirchhoff's current law is the flow quantity, and the product of the pair of the difference quantity and the flow quantity (ie, Pao · Fai, Fbo · Pbi, Fco · Pci) is passed between the component models. Between the component models shown in FIG. 4, the difference amount Pao output from the component model A is distributed and coupled to the difference amounts Pbi and Pci input to the component models B and C, respectively (Pao = Pbi = Pci) On the other hand, the flow amounts Fbo and Fco output from the component models B and C, respectively, are added and combined with the flow amount Fai input to the component model A. Fai = Fbo + Fco). This is because the energy Pao · Fai of the component model A is distributed to the component models B and C by the amount of difference, and the energy of the component models B and C is returned to the component model A by adding Pao · (Fbo + Fco) by the flow amount. Is meant to be.

Ｘｃドットは部品モデルＣに関する状態変数，Ａｃ，Ｂｃ，Ｃｃは係数行列をあらわす。なお、ここでは、説明を簡単化するために、部品モデルＡ，Ｂ及びＣを全て線形システムで表現するため、伝達係数Ｄｘは全て０となる。 The component models A and B are expressed by the same system equations as the above formulas 1 and 2, respectively. In addition, the part model C is expressed by the following system equation, similarly to the part models A and B.
(Formula 8)

Xc dots represent state variables related to the component model C, and Ac, Bc, and Cc represent coefficient matrices. Here, in order to simplify the explanation, the component models A, B, and C are all expressed by a linear system, so that the transfer coefficients Dx are all zero.

  Hereinafter, the part models A, B, and C are combined to create an entity model to be simulated, that is, 2 for deriving the system equations of the entity model based on the system equations of the part models A, B, and C. The street methods (Examples 1 and 2) will be described sequentially.

Example 1
In order to combine the component models having a one-to-many relationship, in the first embodiment, among the component models having a one-to-two relationship, two component models B connected in parallel to the component model A and C is preliminarily combined into one, and then the connection to the component model A is performed in the same manner as the connection of the component models having a one-to-one relationship.

First, the following equation is obtained by combining system equations of models corresponding to the component models B and C so that each coefficient matrix is arranged in a diagonal component direction.
(Formula 9)

Next, based on the condition of Fbco = Fbo + Fco, the following equation is obtained by adding and combining the rows of Fbo and Fco into one row. “Fbco” represents the addition result of outputs from the functional parts B and C, and corresponds to the input flow amount Fai to the part model A.
(Formula 10)

Next, based on the condition of Pbi = Pci = Pbci, the following equation is obtained by adding and combining the columns of Pbi and Pci into one column. “Pbci” represents a distribution input to the component models B and C, and corresponds to the output level difference Pao from the component model A.
(Formula 11)

Subsequently, the following equation is obtained by combining the system equation of the model (B · C) in which the component models B and C are already combined as described above and the system equation of the component model A. Here, both system equations are combined with each other so that each coefficient matrix is arranged in a diagonal component direction.
(Formula 12)

Thereafter, model connection is performed in the same manner as the connection of the part models having the one-to-one relationship described with reference to FIG. 10 based on the conditions of Pbci = Pao and Fbco = Fai. The following combined result is obtained as an equation representing
(Formula 13)

  FIG. 5 is a flowchart of the component model combining process (S23) in the flow of FIG. 3 reflecting the procedure of the first embodiment. In this process, first, a system equation of each part model is input by the user to determine whether or not it is already registered in the model creating apparatus 10 (S31), and as a result, the system equation is not registered. If it is determined, step S31 is repeated. On the other hand, if it is determined that the system equation has already been registered, equations of models other than the reference part model are combined (S32). As a result, an equation corresponding to Equation 9 is obtained.

  Here, the “reference component model” represents a component model corresponding to one of the component models having a one-to-many relationship, and corresponds to the component model A shown in FIG. On the other hand, “other than the reference part model” represents a plurality of part models corresponding to many of the one-to-many part models, and corresponds to the part models B and C in the example shown in FIG. .

  After that, based on the input / output relationship of the amount of difference between the component models and the flow amount, the rows and columns are added and combined, and the rows and columns are reduced (S33). As a result, equations corresponding to Equations 10 and 11 are obtained. Thereafter, the system equation of the model acquired in step S33 is combined with the system equation of the reference part model (S34). In this case, the combination is performed so that the coefficient matrix included in each system equation is arranged in the diagonal component direction. As a result, an equation corresponding to Equation 12 is obtained.

  After step S34, the reference part model and the other part models are combined in the same manner as the part model having the one-to-one relationship described with reference to FIG. Specifically, substitution processing between input and output is performed (S35), and unnecessary columns are deleted along with this substitution processing (S36). Subsequently, it is determined whether or not the substitution process in step S34 has been completed (S37). As a result, it is determined that there are still inputs and outputs to be coupled among the plurality of component models, and the substitution process has not been completed. If YES, the process returns to step S35 and the subsequent steps are repeated. On the other hand, if there is no input / output to be coupled between the plurality of component models and it is determined that the substitution process has been completed, an unnecessary line is subsequently deleted (S38). After step S38, the system equation of the combined model is output (S39). After the above component model combining process, the process returns to the main flow shown in FIG.

  In the first embodiment, when a plurality of part models (corresponding to part models B and C) connected in parallel to one part model (corresponding to part model A) are preliminarily combined into one, Based on the input / output relationship between the amount of difference and the flow amount, the addition of multiple rows and columns to reduce the total number of rows and columns makes subsequent calculations easier and more efficient. Therefore, it can be expected to increase the processing speed.

(Example 2)
In the first embodiment described above, unnecessary columns are deleted for each input / output substitution process (S34 in FIG. 5). However, in the second embodiment, the columns are not deleted during the joining process, and the basic process is performed. Part models that have a typical one-to-one relationship are repeatedly combined, and after all the combining processes are completed, unnecessary columns are deleted, resulting in a plurality of parts having a one-to-many relationship Model coupling is feasible.

First, the following equations are obtained by combining the system equations of the component models A, B, and C expressed by the equations 1, 2, and 8 so that the coefficient matrices are arranged in the diagonal component direction.
(Formula 14)

The following formula is obtained by arranging the above formula 14 in the order of “state variable”, “input variable”, and “output variable”.
(Formula 15)

この数式１６では、上記数式１５に対して、Ｘｂ列及びＸｃ列の１行目にそれぞれ「Ｂａ・Ｃｂ」及び「Ｂａ・Ｃｃ」が追加されている。すなわち、部品モデルＡに関する状態変数Ｘａドットをあらわす方程式に含まれる項Ｂａ・Ｆａｉは、Ｆａｉ＝Ｆｂｏ＋Ｆｃｏの条件に基づき、
Ｂａ・Ｆａｉ＝Ｂａ・（Ｆｂｏ＋Ｆｃｏ）
＝Ｂａ・Ｆｂｏ＋Ｂａ・Ｆｃｏ
＝Ｂａ・（Ｃｂ・Ｘｂ）＋Ｂａ・（Ｃｃ・Ｘｃ）
＝（Ｂａ・Ｃｂ）・Ｘｂ＋（Ｂａ・Ｃｃ）・Ｘｃ
と表すことが可能であるため、上記のように、Ｘｂ列及びＸｃ列の１行目にそれぞれ「Ｂａ・Ｃｂ」及び「Ｂａ・Ｃｃ」を追加することにより、１行目に「Ｂａ」が存在するＦａｉ列を削除することができる。ただし、この実施例２では、計算処理の効率化を図り、この時点で、Ｆａｉ列をそのまま残しておくようにする。 Subsequently, by arranging under the condition of Fai = Fbo + Fco, the above formula 15 is expanded as the following formula in the calculation process.
(Formula 16)

In Equation 16, “Ba · Cb” and “Ba · Cc” are added to the first row of the Xb column and the Xc column, respectively, with respect to Equation 15. That is, the term Ba · Fai included in the equation representing the state variable Xa dot related to the component model A is based on the condition of Fai = Fbo + Fco.
Ba · Fai = Ba · (Fbo + Fco)
= Ba · Fbo + Ba · Fco
= Ba · (Cb · Xb) + Ba · (Cc · Xc)
= (Ba · Cb) · Xb + (Ba · Cc) · Xc
Therefore, as described above, “Ba · Cb” and “Ba · Cc” are added to the first row of the Xb column and the Xc column, respectively, so that “Ba” is added to the first row. An existing Fai column can be deleted. However, in the second embodiment, the calculation process is made more efficient, and at this point, the Fai column is left as it is.

この数式１７では、上記数式１６に対して、Ｘａ列の２行目及び３行目にそれぞれ「Ｂｂ・Ｃａ」及び「Ｂｃ・Ｃａ」が追加されている。すなわち、部品モデルＡに関する状態変数Ｘｂドットをあらわす方程式に含まれるＢｂ・Ｐｂｉは、Ｐａｏ＝Ｐｂｉの条件に基づき、
Ｂｂ・Ｐｂｉ＝Ｂｂ・Ｐａｏ
＝Ｂｂ・（Ｃａ・Ｘａ）
＝（Ｂｂ・Ｃａ）・Ｘａ
と表すことが可能であり、また、部品モデルＡに関する状態変数Ｘｂドットをあらわす方程式に含まれるＢｃ・Ｐｃｉは、Ｐａｏ＝Ｐｃｉの条件に基づき、
Ｂｃ・Ｐｃｉ＝Ｂｃ・Ｐａｏ
＝Ｂｃ・（Ｃａ・Ｘａ）
＝（Ｂｃ・Ｃａ）・Ｘａ
と表すことが可能であるため、上記のように、Ｘａ列の２行目及び３行目にそれぞれ「Ｂｂ・Ｃａ」及び「Ｂｃ・Ｃａ」を追加することにより、Ｐｂｉ列及びＰｃｉ列を削除することができる。ただし、実施例２では、計算処理の効率化を図り、この時点で、Ｐｂｉ列及びＰｃｉ列をそのまま残しておくようにする。 Furthermore, the above formula 15 is expanded as the following formula in the calculation process by organizing under the condition of Pao = Pbi = Pci.
(Formula 17)

In Equation 17, “Bb · Ca” and “Bc · Ca” are added to the second row and the third row of the Xa column, respectively, with respect to Equation 16. That is, Bb · Pbi included in the equation representing the state variable Xb dot related to the component model A is based on the condition of Pao = Pbi,
Bb · Pbi = Bb · Pao
= Bb. (Ca.Xa)
= (Bb · Ca) · Xa
And Bc · Pci included in the equation representing the state variable Xb dot related to the component model A is based on the condition of Pao = Pci,
Bc · Pci = Bc · Pao
= Bc · (Ca · Xa)
= (Bc · Ca) · Xa
Therefore, as shown above, the “Pb” column and the “Pc” column are deleted by adding “Bb · Ca” and “Bc · Ca” respectively to the second and third rows of the Xa column. can do. However, in the second embodiment, the calculation process is made more efficient, and at this point, the Pbi column and the Pci column are left as they are.

Thereafter, the three inputs Fai, Pbi, and Pci are collectively deleted, and the following equation is obtained by deleting the Fai column, the Pbi column, and the Pci column.
(Formula 18)

Thereafter, unnecessary outputs Pao, Fbo, and Fco are deleted, so that the following combined result is finally obtained as an equation representing the real model.
(Formula 19)

  FIG. 6 is a flowchart of the component model combining process (S23) in the flow of FIG. 3 reflecting the procedure of the second embodiment. In this process, first, a system equation of each part model is input by the user to determine whether or not it has been registered in the model creating apparatus 10 (S41). As a result, the system equation is not registered. If it is determined, step S41 is repeated. On the other hand, if it is determined that the system equations are registered, the system equations of the respective component models are combined (S42). In this case, the combination is performed so that the coefficient matrix included in each system equation is arranged in the diagonal component direction. Furthermore, the system equation of each component model after combination is organized based on the input / output relationship between the amount of difference and the flow amount between the component models (S43), and in preparation for the substitution process between input and output performed thereafter, The rows and columns are arranged in the list of input / output variables and state variables.

  Thereafter, substitution processing between input and output is performed (S44). Subsequently, it is determined whether or not the substitution process in step S44 has been completed (S45). As a result, when it is determined that input / output to be coupled between the component models still remains and the substitution process has not been completed, the process returns to step S44, and the subsequent steps are repeated. When it is determined that the input / output to be combined is lost and the substitution process is completed, unnecessary rows and columns are deleted (S46). After step S46, the system equation of the combined model is output (S47). After the above component model combining process, the process returns to the main flow shown in FIG.

  In the above-described first embodiment, in order to combine the component models having a one-to-many relationship, it is necessary to perform addition combination of rows and columns based on the input / output relationship of the amount of difference and the flow amount between the component models. However, in the second embodiment, it is only necessary to perform basic coupling, and as a result, it is possible to realize easy program development and high-speed calculation processing. Currently, an object-oriented language such as C ++ is often used as a programming language, and the object-oriented language has a function of overloading classes and operators not found in other languages. For example, when each component model constituting an actual model to be simulated is expressed by a class and the coupling between classes is expressed by a “+ operator”, for example, when component models A, B, and C are combined, A simple expression such as C = part model A + part model B can express a connection between part models having a one-to-many relationship.

In the following description, an example in which a vehicle body model having a one-to-many relationship and two tire models are combined when modeling a vehicle will be taken up.
FIG. 7 is an explanatory diagram showing the interaction between the vehicle body and the first and second tires at the rear. As shown in this figure, when a torque T is applied to the tire shaft 32 that connects the paired first tire 30L and second tire 30R, a speed V is generated in the vehicle body 20. The speed V output from the vehicle body 20 is transmitted to the first tire 30L and the second tire 30R, and the angular speed W of the tire shaft 32 is thereby generated.

  FIG. 8 is a diagram showing a vehicle body model and two tire models interconnected by a pair of input / output state quantities, reflecting the interaction shown in FIG. As can be seen from FIG. 8, in this case, the force Fbody to the vehicle body 20 is input to the vehicle body model, while the vehicle body speed Vbody is output from the vehicle body model. In addition, a first speed Vtire1 transmitted from the vehicle body 20 to the first tire 30L is input to the first tire model, while a force Ftire1 generated by the first tire 30L is output from the first tire model. Similarly, the second speed Vtire2 transmitted from the vehicle body 20 to the second tire 30R is input to the second tire model, while the force Ftire2 generated by the second tire 30R is output from the second tire 30R. .

  Further, FIG. 9 is a detailed block diagram of a vehicle model constituted by the vehicle body model, the first tire model, and the second tire model connected as shown in FIG. As can be seen from FIG. 9, the vehicle body model, the first tire 30R, and the second tire 30L take into account the characteristic parameters of each component in addition to various state variables and input / output variables. And a system equation for the second tire model.

この式から、

の関係に基づき、次式が得られる。

したがって、車体質量の状態変数Ｘドットｍｂｏｄｙは、車体２０の力及び速度変化率により次式のように表される。

このＸドットｍｂｏｄｙを積分した値が、車体２０の速度Ｘｍｂｏｄｙとなる。 First, the state variable X dot mbody of the vehicle body mass related to the vehicle body model will be described.
When F is force [N], M is mass [kg], and a is acceleration [m / s ² ], the linear equation of motion is as follows.

From this equation:

Based on this relationship, the following equation is obtained.

Therefore, the state variable X dot mbody of the vehicle body mass is expressed by the following equation according to the force and speed change rate of the vehicle body 20.

A value obtained by integrating the X dots mbody is the speed Xmbody of the vehicle body 20.

As can be seen from FIG. 9, the input / output variables of the vehicle body 20 are the speed (Vbody) of the vehicle body 20 and the force input (Fbody) to the vehicle body 20. In addition to this, as a characteristic parameter of the vehicle body 20, a mass (Mb) of the vehicle body 20, a travel resistance coefficient (Db) based on air resistance to the vehicle body 20, and an offset value (Fd) of a travel resistance such as a road surface gradient are taken into consideration. Then, the system equation of the car body model is as follows.
(Formula 20)

この式の変形式Ｗ＝Ｔ／Ｊに基づき、タイヤ回転時の慣性モーメントをＪｔとした場合、タイヤ慣性力の状態変数Ｘドットｊｔｉｒｅは、タイヤ３０Ｌ，３０Ｒに対するトルク及び角速度の変化率により次のように表される。

このタイヤ慣性力の状態変数Ｘドットｊｔｉｒｅを積分した値がタイヤの角速度Ｘｊｔｉｒｅとなる。 Next, the state variable X dot jtire of the tire inertia force related to the tire model will be described.
If T is the rotational torque [N · m], J is the rotational moment [rad / s], and W is the angular velocity change rate [rad / s ² ], the equation of motion of rotation is as follows.

Based on the deformation formula W = T / J of this formula, when the moment of inertia at the time of tire rotation is Jt, the state variable X dot jtire of the tire inertia force depends on the change rate of the torque and the angular velocity with respect to the tires 30L and 30R. It is expressed as follows.

The value obtained by integrating the state variable X dot jtire of the tire inertia force is the tire angular velocity Xjtire.

変位ｘの変化率（距離の時間微分値）は速度ｖであるから、上記式を両辺微分することで、次式が得られる。

フックの法則はねじりバネに関しても同様の式で表現可能であるため、ここでの変位は回転方向の変化量で考える。このねじり変位の変化率（回転の時間微分値）は角速度Ｗｘであるから、上記式より回転トルクの変化率Ｔは次式で表される。

この式に基づき、タイヤ剛性の状態変数Ｘドットｋｔｉｒｅは、タイヤ３０Ｌ，３０Ｒの角速度及びトルクの変化率により次のように表される。

このタイヤ剛性の状態変数Ｘドットｋｔｉｒｅを積分した値がタイヤ３０Ｌ，３０ＲのトルクＸｋｔｉｒｅとなる。 The tire stiffness state variable X dot ktire relating to the tire model will be described.
Assuming that F is a force [N], K is a spring constant [N / m], and x is a displacement [m], Hooke's law concerning the rigidity of an object is as follows.

Since the rate of change of the displacement x (the time differential value of the distance) is the velocity v, the following equation is obtained by differentiating the above equation on both sides.

Hook's law can be expressed by a similar expression for a torsion spring, so the displacement here is considered as the amount of change in the rotational direction. Since the change rate of the torsional displacement (time differential value of rotation) is the angular velocity Wx, the change rate T of the rotational torque is expressed by the following equation from the above equation.

Based on this equation, the tire stiffness state variable X dot ktire is expressed as follows according to the angular velocity and torque change rate of the tires 30L, 30R.

A value obtained by integrating the tire stiffness state variable X dot ktire becomes the torque Xktire of the tires 30L and 30R.

Here, as can be seen from FIG. 9, the input / output variables of the tires 30L and 30R are the angular velocity output (Wtire) of the tire shaft, the torque input (Ttire) applied to the tire shaft, and the speed input transmitted from the vehicle body 20 to the tires 30L and 30R. (Vtire), an output of force generated by the tires 30L and 30R (Ftire). In addition, considering the tire moment of inertia (Jt), the loss resistance (Dt) of the tires 30L and 30R, the tire stiffness (Kt), and the tire radius (Rt) as parameters of the tires 30L and 30R, the tire model The system equation is as follows.
(Formula 21)

  Hereinafter, the process of outputting the system equation of the vehicle model based on the system equation of the vehicle body model expressed by the above formula 20 and the system equation of the first and second tire models expressed by the above formula 21 is described in the above embodiment. A description will be given along the procedures 1 and 2.

In the procedure of the first embodiment, first, the system equations of the first tire model and the second tire model are combined so that the coefficient matrices included therein are arranged in the diagonal component direction, thereby obtaining the following equation. . The first tire and the second tire are distinguished from each other by adding postfixes 1 and 2 to the terms constituting the system equation of the tire model.
(Formula 22)

Next, based on the condition of Ftire12 = Ftire1 + Ftire2, the following equation is obtained by adding and combining the rows of Ftire1 and Ftire2 into one row. “Ftire12” represents an addition result of outputs from the first and second tire models, and corresponds to an input variable Fbody to the vehicle body model.
(Formula 23)

Further, based on the condition of Vtire12 = Vtire1 = Vtire2, the following equation is obtained by adding and combining the columns of Vtire1 and Vtire2 into one column. “Vtire12” represents a distribution input to the first and second tire models, and corresponds to an output variable Vbody from the vehicle body model.
(Formula 24)

Subsequently, the following equation is obtained by combining the system equation of the model expressed by Equation 24 and the system equation of the vehicle body model A expressed by Equation 20 in which the first and second tire models are combined.
(Formula 25)

Furthermore, by executing the substitution process based on the condition of Vtire12 = Vbody, the Vtile12 column can be deleted, and the following expression is obtained.
(Formula 26)

Subsequently, by executing substitution processing based on the condition of Fbody = Ftire12, the Fbody column can be deleted, and the following expression is obtained.
(Formula 27)

By rearranging the above equation 27, the following equation is obtained.
(Formula 28)

Finally, the unnecessary output is deleted from the equation 28, and the following equation is obtained as a result of combining the vehicle body model and the first and second tire models having a one-to-many relationship.
(Formula 29)

On the other hand, in the procedure of Example 2, first, the system equations of the vehicle body model, the first tire model, and the second tire model are combined so that each coefficient matrix is arranged in the diagonal component direction. The following equation is obtained.
(Formula 30)

Next, the following equation is obtained by arranging the above equation 30 in the order of “state variable”, “input variable”, and “output variable”.
(Formula 31)

この数式３２では、上記数式３１に対して、Ｘｋｔｉｒｅ１列及びＸｋｔｉｒｅ２列の１行目にそれぞれ「Ｒｔ１／Ｍｂ」及び「Ｒｔ／Ｍｂ」が追加されており、また、実質的には削除されるべきＦｂｏｄｙ列が削除されずにそのまま残されている。 Subsequently, by arranging under the condition of Fbody = Ftire1 + Ftire2, the above formula 31 is expanded as the following formula in the calculation process.
(Formula 32)

In the equation 32, “Rt1 / Mb” and “Rt / Mb” are added to the first row of the Xktire1 column and the Xktire2 column, respectively, with respect to the equation 31, and should be substantially deleted. The Fbody column is left without being deleted.

この数式３３では、上記数式３２に対して、Ｘｍｂｏｄｙ列の３行目及び５行目にそれぞれ、「−Ｋｔ１・Ｒｔ１」及び「−Ｋｔ２・Ｒｔ２」が追加されており、また、実質的には削除されるべきＶｔｉｒｅ１列及びＶｔｉｒｅ２列が削除されずにそのまま残されている。 After that, the above equation 32 is expanded as the following equation in the calculation process by arranging under the condition of Vtire = Vtire2 = Vbody.
(Formula 33)

In the equation 33, “−Kt1 · Rt1” and “−Kt2 · Rt2” are added to the third row and the fifth row of the Xmbody column, respectively, with respect to the equation 32. The Vtire1 column and the Vtile2 column to be deleted are left without being deleted.

Then, the following expression is obtained by deleting three inputs of Vtire1, Vtire2, and Fbody, and deleting the Vtire1, Vtire2, and Fbody columns together.
(Formula 34)

Finally, by deleting unnecessary output from the above equation 34, the following equation is obtained as a result of combining the vehicle body model and the first and second tire models having a one-to-many relationship.
(Formula 35)

  As described above, when there are three or more component models that are related to each other as elements constituting the actual model to be simulated, by combining the component models according to the procedure of the first and second embodiments described above. , Each part model can be modeled separately, which enables modeling according to various needs, such as modeling considering only a part of the vehicle's four wheels (for example, two wheels) It becomes. Further, in the case of the first embodiment, when a plurality of component models connected in parallel to one component model are preliminarily combined into one, a plurality of components models are based on the relationship of input / output state quantities between the component models. In order to reduce the total number of rows and columns, and in the case of the second embodiment, one type of basic joining process is repeated, which is unnecessary after the completion of all the joining processes. Therefore, it is possible to more easily and efficiently execute the calculation process for combining the component models.

It should be noted that the present invention is not limited to the illustrated embodiments, and it goes without saying that various improvements and design changes can be made without departing from the scope of the present invention.
For example, in the above-described embodiment, an example in which a vehicle model is created as an example of an entity model is taken. However, the present invention is not limited to this, and the present invention is not limited to any model as long as it is a model composed of a plurality of component models. It can also be applied to the creation of an entity model.

It is a figure which shows the hardware constitutions of the model production apparatus which concerns on embodiment of this invention. It is explanatory drawing showing the simulation performed based on a simulation program in the said model production apparatus by making vehicle running simulation into an example. It is a flowchart about the simulation performed based on the said simulation program. It is a figure which shows the component models A, B, and C mutually connected by the pair of input-output state quantity, being applied to the 1-to-2 relationship. It is a detailed flowchart about the connection process (S23 in FIG. 3) of the part model which concerns on Example 1 of this invention. It is a detailed flowchart about the coupling | bonding process (S23 in FIG. 3) of the component model which concerns on Example 2 of this invention. It is explanatory drawing showing the interaction between a vehicle body and the 1st tire and 2nd tire of a rear part. FIG. 8 is a diagram illustrating a vehicle body model, a first tire model, and a second tire model that are connected to each other by pairs of input / output state quantities, reflecting the interaction shown in FIG. 7. It is a detailed block diagram of a vehicle model configured by a vehicle body model, a first tire model, and a second tire model. It is a figure which shows notionally the component model mutually connected by the pair of input-output state quantity, being applied to the one-to-one relationship.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 ... CPU, 2 ... ROM, 3 ... RAM, 4 ... Hard disk (HD), 5 ... Interface part (I / F), 6 ... Display part, 7 ... Input part, 8 ... Optical disk drive, 9 ... Optical disk, 10 ... Model creation device, 20 ... body, 30L ... first tire, 30R ... second tire.

Claims (2)

A simulation execution device in which a part model corresponding to a plurality of parts set independently for each predetermined function as an element constituting an entity to be simulated is registered,
The part model includes a vehicle body model and a tire model that constitute a vehicle, and the system equation of each part model represents a state quantity that represents a potential difference and a flow component that represent a potential component of energy applied to the part. As a flow quantity as a pair of input and output state quantities, the parameters of the internal characteristics of the component to which the input and output state quantities are added are arranged in a matrix format in which rows are output state vectors and columns are input state vectors. , Expressed as an internal matrix corresponding to the above-mentioned difference amount and flow amount,
The vehicle body model is a first system equation of the vehicle body expressed as a linear equation.

(Here, the state variable of the vehicle body mass (X dot mbody) is included as the state variable, and the vehicle body speed (Vbody) and the force input to the vehicle body (Fbody) are included as the input / output variables of the vehicle body. as a parameter, it includes vehicle mass (Mb), running resistance coefficient based on the air resistance to the vehicle body (Db), include an offset value of the running resistance of the road surface slope or the like (Fd) is),
The tire model is a second system equation of the tire expressed as a linear equation.

(Here, the state variable X dot jtire and the tire stiffness state variable X dot ktire are included as the state variables, and the tire shaft angular velocity output (Wtire) and the tire shaft are added as tire input / output variables. It includes torque input (Ttire), speed input transmitted from the vehicle body to the tire (Vtire), and output of the force generated by the tire (Ftire). As tire characteristic parameters, tire inertia moment (Jt), tire loss resistance ( Dt), tire stiffness (Kt) and tire radius (Rt) are included) ,
The simulation execution device is
When receiving an instruction to create a vehicle simulation model using the vehicle body model and a plurality of the tire models constituting a vehicle, the vehicle body model and the tire model are automatically integrated, and each component by setting the position difference amount and flow amount of the input-output relationship between the models, the vehicle simulation model generating means in which a plurality of the tire model in the vehicle body model to create a vehicle simulation model coupled in parallel,
Parameter input means for inputting parameters relating to the vehicle body and tires constituting the vehicle;
Test condition data input means for inputting test conditions in an actual vehicle running test,
Driving operation data input means for inputting driving operation in an actual vehicle running test,
The simulation execution means for executing the simulation of the vehicle simulation model created by the vehicle model creation means based on the input parameters, test conditions and driving operation,
The vehicle simulation model creation means includes
The computer combines the second system equations of the N tire models (N> 1) , and in the combined system equation,
Ftire _composite = Ftire ₁ + Ftire ₂ + ... + Ftire _N-1
Vtire _composite = Vtire ₁ = Vtire ₂ = ... = Vtire _N-1
(Where suffix 1 to N-1 distinguish N-1 tire models , Ftire _composite is a force input generated by the following composite model, and Vtire _composite is based on the speed input) transmitted from the vehicle body to the tire, the rows and columns by computer summing junction, of one composite model corresponding to a plurality of the tire model, the system equation is expressed using the vectors and matrices First combining means to configure;
And system equation of the composite model, the first system equations in combination computer of the vehicle body model, the vehicle simulation model, a second combining means for creating a system equation that is expressed using the vectors and matrices,
In the system equation of the above vehicle simulation model , the following relational expression Fbody = Ftire _compound
Vbody = Vtire _composite
Based on the above, the substitution processing means for automatically performing substitution processing in which the computer automatically substitutes the output of the component model of the coupling source to the input of the component model that is the coupling destination ,
In the system equation of the vehicle simulation model expressed using a vector and a matrix for each substitution process, the computer automatically deletes a column in which all elements are zero ,
A simulation execution apparatus characterized by comprising: A simulation execution device in which a part model corresponding to a plurality of parts set independently for each predetermined function as an element constituting an entity to be simulated is registered,
The part model includes a vehicle body model and a tire model that constitute a vehicle, and the system equation of each part model represents a state quantity that represents a potential difference and a flow component that represent a potential component of energy applied to the part. As a flow quantity as a pair of input and output state quantities, the parameters of the internal characteristics of the component to which the input and output state quantities are added are arranged in a matrix format in which rows are output state vectors and columns are input state vectors. , Expressed as an internal matrix corresponding to the above-mentioned difference amount and flow amount,
The vehicle body model is a first system equation of the vehicle body expressed as a linear equation.

(Here, the state variable of the vehicle body mass (X dot mbody) is included as the state variable, and the vehicle body speed (Vbody) and the force input to the vehicle body (Fbody) are included as the input / output variables of the vehicle body. as a parameter, it includes vehicle mass (Mb), running resistance coefficient based on the air resistance to the vehicle body (Db), include an offset value of the running resistance of the road surface slope or the like (Fd) is),
The tire model is a second system equation of the tire expressed as a linear equation.

(Here, the state variable X dot jtire and the tire stiffness state variable X dot ktire are included as the state variables, and the tire shaft angular velocity output (Wtire) and the tire shaft are added as tire input / output variables. It includes torque input (Ttire), speed input transmitted from the vehicle body to the tire (Vtire), and output of the force generated by the tire (Ftire). As tire characteristic parameters, tire inertia moment (Jt), tire loss resistance ( Dt), tire stiffness (Kt) and tire radius (Rt) are included) ,
The simulation execution device is
When receiving an instruction to create a vehicle simulation model using the vehicle body model and a plurality of the tire models constituting a vehicle, the vehicle body model and the tire model are automatically integrated, and each component by setting the position difference amount and flow amount of the input-output relationship between the models, the vehicle simulation model generating means in which a plurality of the tire model in the vehicle body model to create a vehicle simulation model coupled in parallel,
Parameter input means for inputting parameters relating to the vehicle body and tires constituting the vehicle;
Test condition data input means for inputting test conditions in an actual vehicle running test,
Driving operation data input means for inputting driving operation in an actual vehicle running test,
The simulation execution means for executing the simulation of the vehicle simulation model created by the vehicle model creation means based on the input parameters, test conditions and driving operation ,
The vehicle simulation model creation means includes
The second system equations of the tire model of the first system equations and N one of said vehicle body model (N> 1) in combination computer, the vehicle simulation model, the system equation is expressed using the vectors and matrices Combination means to create ;
In the system equation of the vehicle simulation model ,
Fbody = Ftire ₁ + Ftire ₂ + ... + Ftire _N-1
Vbody = Vtire ₁ = Vtire ₂ = ... = Vtire _N-1
(Where the suffixes 1 to N-1 distinguish N-1 tire models , the Ftire _compound is a force input generated by the vehicle simulation model, and the Vtire _compound is derived from the vehicle body of the vehicle simulation model. Substitution processing means in which the computer automatically performs substitution processing for substituting the output of the component model of the coupling source into the input of the component model that is the coupling destination, based on the speed input transmitted to the tire )
And a deletion means for automatically deleting a column in which all elements are zero in the system equation of the vehicle simulation model expressed by using a vector and a matrix for each substitution process. Simulation execution device.

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