JP2003139627A - Method for finding physical quantity - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a method for finding physical quantities such as stress components σx , σy , σz , τxy , τyz , τzx , etc., with a high precision in a short time by positively using, for computation, information on conventional boundary conditions (i.e., estimated actual external forces) which have not been used until now. SOLUTION: This method is provided with a step for making a first map which represents the difference between a main stress sum map of each nodal point formed by computation from the boundary conditions, and a measured main stress sum map of each nodal point found from infrared stress images, a step for making a second map which represents the difference between a main stress sum map of each nodal point found by computation from the boundary conditions, and a main stress sum map of each nodal point obtained when a predetermined force is superposed on a specific external force in an internal region computed form the boundary conditions, and a step for finding an external force distribution which gives a map of main stress sum differences as near as possible to the first map, by the principle of superposition and a least square, utilizing the second map.

Description

Detailed Description of the Invention

[0001]

TECHNICAL FIELD The present invention relates to a value of a first physical quantity measured in an actual object and a value of a first physical quantity estimated by a numerical analysis using a model and parameters of the same shape as the actual object. The present invention also relates to a method of obtaining the value of the second physical quantity in the actual product, and more particularly to a method of obtaining the stress distribution of the elastic body from the temperature change pattern data of the elastic body surface due to the thermoelastic effect and the analysis data obtained by numerical stress analysis.

[0002]

2. Description of the Related Art The stress at any one point of an elastic body is
Expressed in (x, y, z) Cartesian coordinates, it is generally represented by six components, σ _x , σ _y , σ _z , τ _xy , τ _yz , and τ _zx . Of these, σ _x , σ _y , and σ _z are x,
A normal stress component acting on a plane perpendicular to the y and z axes, τ _xy
Is a shear stress that acts in the y direction on a plane where x = constant and in the x direction on a plane where y = constant, and τ _yz and τ _zx
Is also a shear stress that follows the same definition for subscripts. If an appropriate coordinate system is selected for that point, all shear stress components will disappear and only normal stress components will exist. The normal stress components will be the principal stress components σ ₁ , σ ₂ , and σ _3.
Called.

By the way, it has been known by Weber, Kelvin and others since the 19th century that the temperature change occurs in proportion to the adiabatic stress change to an elastic body, which is a thermoelastic effect. . Letting ΔT be the temperature difference before and after applying stress due to this thermoelastic effect, there is a relationship of ΔT = −KT (σ ₁ + σ ₂ + σ ₃ ).
Here, K is a thermoelastic constant that is specific to the material, and T is an absolute temperature. Here, the sum of principal stresses (σ ₁ + σ ₂ + σ
₃ ) is the first-order stress invariant, which has coordinate axes (x, y,
It is proved by the theory of elasticity that it is equal to (σ _x + σ _y + σ _z ), regardless of how z) is taken. ΔT is proportional to the sum of principal stresses because the change in the volume of the elastic body is determined by the first-order stress invariant, and the shear stress component τ _xy ,
This is because the volume change of the elastic body does not occur depending on τ _yz and τ _zx .

The applicant of the present invention utilizes this thermoelastic effect to
A method for easily measuring the stress distribution by repeatedly applying a compressive / tensile load to an elastic body and detecting the temperature change pattern of the elastic body surface accompanying it is disclosed in JP-B-62-1204-5 and 63-63- 7333 and the like.

On the other hand, finite element method, boundary element method, difference method and the like are known as methods for numerically determining the stress distribution of an elastic body. These are numerical analysis methods in which an elastic constant and an external force to be applied are given as boundary conditions to a model having the same shape as an actual object, and stress distributions inside the elastic body and its surface are approximately obtained.

As described above, the temperature change pattern on the surface of the elastic body due to the thermoelastic effect is the sum of principal stresses (σ ₁ + σ ₂ +
Although it is proportional to the distribution of σ ₃ ), from this temperature change pattern data, stress components σ _x , σ _y , σ _z , τ _xy ,
It is not possible to separately know τ _yz and τ _zx . On the other hand, in numerical stress analysis methods such as the finite element method,
It is not easy to give the boundary conditions properly, and therefore it is not always certain that the obtained results correspond to the stress distribution of the real thing.

In order to solve such a problem, Japanese Patent No. 2698029 proposes the following method. FIG. 1 shows a flow chart of a method for separately obtaining stress components σ _x , σ _y , σ _z , τ _xy , τ _yz , and τ _zx from a temperature change pattern of an elastic body surface.

As a premise of this method, a real elastic body is used.
The temperature change pattern when a predetermined stress change is given is
Japanese Patent Publication Nos. 62-1204-5 and 63-73 by the applicant
It is detected by the method utilizing the thermoelastic effect such as No. 33,
From the pattern data, the
Force sum (σ₁+ Σ_Two+ Σ_Three) Distribution is calculated in advance
(Note that this principal stress sum (σ₁+ Σ_Two+ Σ_Three)
Is (σ_x+ Σ_y+ Σ _z)be equivalent to. ). Also this fruit
The elastic constant is given to the model of the shape corresponding to the object, and its boundary
By applying an external force as a boundary condition to the model
The stress distribution inside and on the surface of the
It should be obtained by stress analysis.

First, in step 1, for example, Japanese Patent Publication Sho
62-1204-5, 63-7333, etc.
Using the thermoelastic effect, the temperature change Δ of the actual surface
T pattern is detected, and then in step 2, ΔT
= -KT (σ₁+ Σ_Two+ Σ_Three) Of the actual surface
Principal stress sum (σ_x+ Σ_y+ Σ_z= Z (j)). Furthermore
Then, in step 3, with the actual product for which this principal stress sum was obtained,
Coordinates of nodes and constraints required for numerical stress analysis of models of the same shape
Bundle condition, elastic constant (Young's modulus, Poisson's ratio, etc.), external force P
The coordinates of (i), the master at the interior point j obtained in step 2
Enter the force sum Z (j). Then, in step 4,
For example, applying the finite element method and performing numerical stress analysis,
Principal stress sum F when P (i) = 1 is applied to one fixed external force
Find (i, j). At this time, the elastic body maintains the balance condition
Constrain any part of the boundary like
The force acting on the node is correct when the solution is finally obtained.
I can find a good value. ). And in step 5, this
From Z (j) and F (i, j), the superposition principle and minimum
By the multiplication method, the principal stress sum near the measured principal stress sum distribution Z (j)
The distribution of the external force P (i) that gives the cloth is obtained. Then step
In P6, the external force distribution P obtained in Step 5
From (i), the stress component σ is obtained by numerical stress analysis. _x, Σ_y,
σ_z, Τ_xy, Τ_yz, Τ_zxAnd so on.

[0010]

In such a method, stress components σ _x , σ _y , σ _z , which are applied to the object,
When obtaining τ _xy , τ _yz , τ _zx, etc., each time,
It is difficult to actually make and experiment with the target object, so it takes a lot of time and money, so recently, using a rapidly developing computer, a model of the same shape as the target object is virtually stored in the computer. Nodal coordinates, constraint conditions, material constants, external force applied coordinates, which are necessary for numerical stress analysis.
The principal stress sum at the inner points is input, and the principal stress sum at a plurality of nodes set in the model of the same shape as the target object is being calculated.

However, the method of Japanese Patent No. 2698029
So the traditional boundary conditions (ie
Force is not used in the calculation and the measured infrared
Equivalent to the boundary condition of the finite element method only from force device data
And the created pseudo-boundary line.
The stress component σ_x, Σ_y, Σ_z, Τ_xy, Τ
_yz, Τ_zxSince we are seeking
There is noise in the data of the infrared stress device,
When the number of target nodes is small, it is finally correct.
It was often difficult to derive boundary conditions.

However, recently, as a result of the accumulation of research, the calculation accuracy of the finite element method using the information of the conventional boundary condition (that is, the predicted actual external force) is significantly improved, and the accuracy of 100% is impossible. Even so, the correct results are being obtained with an accuracy of about 80%. Therefore, the stress components σ _x , σ _y , σ _z , τ _xy ,
When obtaining τ _yz , τ _zx, etc., it is more convenient to positively use the calculation result of the finite element method using the information of the conventional boundary condition (that is, the predicted actual external force). Is being considered.

In view of the above points, an object of the present invention is to use the information of the conventional boundary condition (that is, the predicted actual external force), which has never been used so far, for the purpose of calculation. It is to provide a method for obtaining physical quantities such as stress components σ _x , σ _y , σ _z , τ _xy , τ _yz , and τ _zx with high accuracy and in a short time.

[0014]

In order to achieve this object, a method for obtaining a physical quantity according to the present invention is a method in which a surface distribution of a first physical quantity is measured from an actual object, and a model having the same shape as the actual object. In a second step, a second step of estimating a surface distribution of the first physical quantity by a numerical analysis using the and the parameter, a surface distribution of the first physical quantity measured from an actual object in the first step, and a second step The third step of obtaining the difference between the surface distribution of the first physical quantity estimated by the numerical analysis using the model and the parameter of the same shape as the actual object, and the model and the parameter of the same shape as the actual object in the second step. First estimated by numerical analysis using
Determining a difference between the surface distribution of the physical quantity and the surface distribution of the first physical quantity estimated when the value of the specific parameter among the parameters set in the second step is changed by a predetermined amount. Of the first physical quantity obtained in the third step by the superposition principle and the least squares method using the value of the difference in the surface distribution of the first physical quantity obtained in the step of A fifth step of obtaining the value of the parameter that gives the difference value as close as possible to the difference value of the surface distribution,
And a sixth step of obtaining a value of the second physical quantity from the obtained value of the parameter.

Further, the first step of detecting the temperature change pattern of the real surface due to the thermoelastic effect by adiabatically applying stress change to the real elastic body, and the detected temperature change pattern, at the inner point of the real surface The second step of obtaining the principal stress sum, and the third step of inputting the nodal coordinates, constraint conditions, elastic constants, coordinates to which external force is applied, and principal stress sum at the inner point, which are necessary for numerical stress analysis of a model of the same shape as the real thing. And the boundary condition is input, the fourth step of calculating the sum of principal stresses on a plurality of nodes set in the model having the same shape as the actual object by calculation, and the calculation of the boundary condition of each node The fifth step of creating a first map showing the difference between the principal stress sum map and the measured principal stress sum map of each node obtained from the infrared stress image, and the principal stress sum of each node obtained by calculation from boundary conditions From the map and boundary conditions A sixth step of making a second map representing the difference between the principal stresses sum map of each node when the particular external force calculated by internal region overlapped with the predetermined force, the second
From the obtained external force distribution, the seventh step of obtaining the external force distribution that gives the map of the difference of the principal stress sums as close as possible to the first map by the superposition principle and the least squares method using the map of And an eighth step of obtaining a stress component on the node.

[0016]

BEST MODE FOR CARRYING OUT THE INVENTION Embodiments of the present invention will be described below with reference to the drawings. FIG. 2 shows an embodiment of a method for obtaining a physical quantity according to the present invention. As an example thereof, stress components σ _x , σ _y , σ _z , τ _xy are calculated from a temperature change pattern on the surface of an elastic body. , Τ _yz and τ _zx are separately obtained.

As a premise of this method, the temperature change pattern when a predetermined stress change is applied to the real elastic body is as follows: Japanese Patent Publication Nos. 62-12054-5 and 63-73.
It is detected by the method utilizing the thermoelastic effect such as No. 33,
From the pattern data, the distribution of the principal stress sum (σ ₁ + σ ₂ + σ ₃ ) on the actual surface of the elastic body is obtained in advance (note that the principal stress sum (σ ₁ + σ ₂ + σ ₃ ) is (σ
_x + σ _y + σ _z ). ). Also, by giving an elastic constant to the model of the shape corresponding to this real thing and applying an external force to the boundary as a boundary condition, the stress distribution inside the model and on the surface can be obtained by numerical stress analysis such as the finite element method. I shall.

First, in step 1, the temperature change Δ of the actual surface is utilized by utilizing the thermoelastic effect, for example, by using the method of JP-B-62-1204-5 and 63-7333.
T pattern is detected, and then in step 2, ΔT
= −KT (σ ₁ + σ ₂ + σ ₃ ), the principal stress sum (σ _x + σ _y + σ _z = Z (j)) of the surface of the actual object is obtained. Further, in step 3, the coordinates of the nodes, the constraint conditions, the elastic constants (Young's modulus, Poisson's ratio, etc.), the external force P, which are necessary for the numerical stress analysis of the model having the same shape as the actual product for which this principal stress sum is obtained,
The coordinate of (i), the principal stress sum Z (j) at the inner point j obtained in step 2 is input. Then, in step 4,
For example, the finite element method is applied, conventional boundary conditions (that is, predicted actual external forces) are input, and the principal stress sum of the stress measurement site is calculated by numerical stress analysis.

Next, in step 5, step 1,
In step 2, the surface distribution (map) of the measured principal stress sum of each node obtained from the infrared stress image, and in step 4 of each node calculated by the conventional boundary condition (that is, the predicted actual external force) A map A (j) of the difference between the principal stress sum and the surface distribution (map) is created. This is a work for clarifying the deviation between the calculated principal stress sum calculated with an accuracy of about 80% and the measured principal stress sum obtained from the infrared stress image. Next, in step 6, in step 4, the surface distribution (map) of the principal stress sum of each node calculated by the conventional boundary condition (that is, the predicted actual external force) and the conventional boundary condition (ie, , A predicted actual external force), a map B (i, of the difference between the surface distribution (map) of the principal stress sum when a unit force 1 is superimposed on a specific external force P (i) in the internal region calculated Make j). This is a work for systematically knowing what kind of change appears in the surface distribution (map) of the principal stress sum when the unit force 1 is superimposed on the specific external force P (i). It should be noted that the value to be superimposed on the external force P (i) is set to the unit force 1 in the above description, but this does not necessarily mean that the value is limited to this value, and it may be any value. Needless to say. Next, in step 7, using the map B (i, j) of the difference in the principal stress sum, the map A of the difference in the principal stress sum is calculated by the superposition principle and the least squares method.
An external force distribution P (i) that gives a map of the difference between the principal stress sums as close as possible to (j) is determined. These steps 5-7
This is a new point that the conventional method does not have.

Then, in step 8, step 7
The stress components σ _x , σ _y , σ _z , τ _xy , τ _yz , τ are calculated by numerical stress analysis from the external force distribution P (i) determined by
_{Find zx,} etc.

In the above embodiment, the temperature change on the surface of the elastic body is changed.
Component, the stress component σ_x, Σ _y, Σ_z, Τ_xy,
τ_yz, Τ_zxHow to separate and obtain each
However, the present invention is not limited to this.
That is, the only physical quantity that can be calculated by the finite element method is stress.
is not. In addition to stress, strain, temperature, electromagnetic
What physical quantities are available
All of the physical quantities that can be calculated by the finite element method are
Are the subject of the present invention.

FIG. 3 shows another embodiment according to the present invention. As an example thereof, a flow chart of a method for separating the second physical quantity from the surface distribution of the first physical quantity to obtain the second physical quantity is shown. It is shown.

As a premise of this method, it is assumed that the surface distribution of the first physical quantity is obtained in advance from the actual object to be measured. Further, by giving a predetermined parameter to a model having a shape corresponding to this real object, the distribution of the first physical quantity inside and on the surface of the model can be obtained by numerical stress analysis such as the finite element method.

First, in step 1, the surface distribution Z (j) of the first physical quantity is measured from the actual object to be measured.
Next, in step 2, a model having the same shape as the real object to be measured is given a predetermined parameter on a computer to obtain a first physical quantity distribution Z ′ (j) inside and on the surface of the model. calculate. Commercially available numerical stress analysis software such as the finite element method is used for this calculation.

Next, in step 3, the first surface distribution Z (j) of the measured first physical quantity obtained from the actual object and the first estimation estimated by the numerical analysis using the model and parameters of the same shape as the actual object The difference A (j) from the surface distribution Z ′ (j) of the physical quantity is calculated. This is the first calculated with an accuracy of about 80%
This is a work for clarifying the discrepancy between the calculated value of the physical quantity and the measured value of the first physical quantity obtained by the measurement of the actual object. Next, in step 4, the surface distribution Z ′ (j) of the first physical quantity estimated by the numerical analysis using the model having the same shape as the object and the parameter, and the specific parameter i among the set parameters The difference B between the surface distribution Z ″ (j) of the first physical quantity estimated when the value of is changed by a predetermined amount
Find (i, j). This is an operation for systematically knowing what kind of change appears in the surface distribution of the first physical quantity when the unit quantity 1 is superimposed on the specific parameter i.
The value to be superimposed on the parameter i is set to the unit amount 1 in the above description, but this does not necessarily mean that the value is limited to this value, and it goes without saying that it may be any value. Next, in step 5, using the difference B (i, j) of the first physical quantities, the calculated value of the first physical quantity calculated by the superposition principle and the least squares method and the actual measurement are obtained. Difference A from the measured value of the first physical quantity A
The value of the parameter i that gives the difference of the first physical quantity as close as possible to (j) is obtained. These steps 3 to 5 are new points that the conventional method does not have.

Then, in step 6, step 5
The value of the second physical quantity is obtained by numerical stress analysis from the value of the parameter i determined in.

[0027]

As described above, according to the method for obtaining a physical quantity of the present invention, the surface of the first physical quantity estimated by the numerical analysis such as the finite element method using the model having the same shape as the actual object and the parameters. By using the difference between the distribution and the surface distribution of the first physical quantity estimated when the value of the specific parameter among the set parameters is changed by a predetermined amount, the superposition principle and the least squares method are used. , The first estimated by numerical analysis using the surface distribution of the measured first physical quantity obtained from the actual object and the model and parameters of the same shape as the actual object
Since the value of the parameter that gives a difference value as close as possible to the surface distribution of the physical quantity of is determined, it is possible to obtain the value of the second physical quantity with high accuracy in a short time. became.

[Brief description of drawings]

FIG. 1 is a diagram showing a conventional method for obtaining a physical quantity.

FIG. 2 is a diagram showing an embodiment of a method for obtaining a physical quantity according to the present invention.

FIG. 3 is a diagram showing another embodiment of the method for obtaining a physical quantity according to the present invention.

Claims (2)

[Claims] 1. A first step of measuring a surface distribution of a first physical quantity from an actual object and a first step of estimating a surface distribution of the first physical quantity by a numerical analysis using a model and parameters having the same shape as the actual object. The second step, the surface distribution of the first physical quantity measured from the real object in the first step, and the first step estimated by the numerical analysis using the model and the parameter of the same shape as the real object in the second step. A third step of obtaining a difference between the physical quantity and the surface distribution, a first physical quantity surface distribution estimated by a numerical analysis using a model and a parameter having the same shape as the actual object in the second step, and a second step. Of the parameters set in the step, a fourth step of obtaining a difference from the surface distribution of the first physical quantity estimated when the value of the specific parameter is changed by a predetermined amount, and a fourth step Be Using the value of the difference between the surface profile of the first physical quantity, the superposition principle and method of least squares, the third
The step of obtaining the value of the parameter that gives a difference value as close as possible to the value of the difference of the surface distribution of the first physical quantity obtained in the step, and the value of the second physical quantity from the obtained value of the parameter. And a sixth step of obtaining a physical quantity. 2. A first step of detecting a temperature change pattern of a real surface due to a thermoelastic effect by adiabatically applying a stress change to an elastic body, and from the detected temperature change pattern,
The second step to find the sum of principal stresses at the inner points of the real surface, and the nodal coordinates, constraint conditions, elastic constants, external force applied coordinates, and principal stresses at the inner points, which are necessary for numerical stress analysis of a model of the same shape as the real object. The third step of inputting the sum, the fourth step of inputting the boundary conditions and calculating the sum of principal stresses on a plurality of nodes set in the model of the same shape as the real thing, and calculating from the boundary conditions The fifth step of making the first map showing the difference between the principal stress sum map of each node obtained in step 1 and the measured principal stress sum map of each node obtained from the infrared stress image, and the calculation from boundary conditions A second map is created that represents the difference between the principal stress sum map of each node and the principal stress sum map of each node when a predetermined force is superimposed on a specific external force of the internal region calculated from the boundary conditions. Overlap using 6 steps and 2nd map By Align principles and the method of least squares,
The method further comprises a seventh step of obtaining an external force distribution that gives a map of differences in principal stress sums as close as possible to the first map, and an eighth step of obtaining a stress component on any node from the obtained external force distribution. A method of obtaining a physical quantity characterized by that.