CN111475893B - Spatial fault field model construction method based on product three-dimensional model - Google Patents

Spatial fault field model construction method based on product three-dimensional model Download PDF

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CN111475893B
CN111475893B CN202010258235.6A CN202010258235A CN111475893B CN 111475893 B CN111475893 B CN 111475893B CN 202010258235 A CN202010258235 A CN 202010258235A CN 111475893 B CN111475893 B CN 111475893B
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product
fault
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field intensity
cylinder
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CN111475893A (en
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杨德真
任羿
王自力
冯强
孙博
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Beihang University
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    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
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    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q30/00—Commerce
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    • G06—COMPUTING; CALCULATING OR COUNTING
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Abstract

The invention relates to a spatial fault field model construction method based on a product three-dimensional model. The method is based on the concept of field, the fault mode distribution of the product composition units is visualized, and the fault mode distribution is radiated to the surface of the product to form a fault field, so that a basis is provided for the maintainability design of the product. It comprises three steps: (1) calculating the risk index of each unit and each fault mode of the product, namely determining the risk index of each fault mode of each component unit according to the analysis result of the influence and the hazard of the fault modes; (2) calculating the spatial fault field intensity of the product composition unit, namely calculating by combining the fault mode risk index and the unit maintenance difficulty; (3) and calculating the surface fault field intensity of the product, namely converting the irregular units into a regular three-dimensional line frame body, and then projecting the unit space fault field intensity to the surface of the product to form a fault field distribution model. The product maintenance flap design can be guided based on the model.

Description

Spatial fault field model construction method based on product three-dimensional model
Technical Field
The method for constructing the space fault field model based on the three-dimensional model of the product realizes the visual expression of the product fault information on the surface of the product, thereby providing guidance for the design of a product maintenance cover. The invention belongs to the technical field of reliability engineering.
Background
Maintenance flap design is one of the important aspects in design, and in order to ensure that the product is maintained and repaired in time during use, the flap needs to be opened on the surface of the product. The quality of the flap design is directly related to the level of maintainability of the product. Current flap designs, while simple to consider, are economical and accessible, do not have a good way to accurately guide maintenance flap design. In view of the above, the invention introduces the concept of 'field', combines the product failure mode influence and the harmfulness analysis (FMECA) result, and designs a spatial failure field model construction method based on a product three-dimensional model. The method can comprehensively consider the occurrence probability, the severity category and other factors of each fault mode of the product, and the factors are expressed on the surface of the product and overlapped to form the fault field intensity, so that the distribution condition of fault information on the surface of the product is visually described, and a designer is guided to reasonably design the position and the size of the cover.
Disclosure of Invention
The invention aims to realize the visual expression of product fault information on the surface of a product and provide guidance for the design of a product maintenance cover.
The invention provides a method for constructing a space fault field model based on a three-dimensional model of a product, which mainly comprises the following steps:
the method comprises the following steps: and calculating the risk index of each unit and each failure mode of the product.
And calculating the risk index of each component unit and each fault mode of the product according to the result of the fault mode influence and hazard analysis (FMECA) of the product, wherein the risk index is determined by the occurrence probability level, the severity level and the detection difficulty level of the fault mode.
Step two: and calculating the spatial fault field intensity of the product composition unit.
The space fault field intensity is a quantitative index for comprehensively describing the fault mode risk index and the maintenance difficulty of the unit. The cell space fault field intensity is superposed by the fault field intensity of the cell fault mode. This step comprises 3 sub-steps:
step 1: the fault field strength of each fault mode in the product component is calculated and is determined by the risk index of each fault mode.
Step 2: and calculating the maintenance difficulty of each product composition unit. For a product component, the difficulty of repair can be measured by accessibility and detachability. The better the accessibility, the lower the maintenance difficulty; the better the detachability, the lower the difficulty of maintenance.
And step 3: and calculating the spatial fault field intensity of each product composition unit. The unit space fault field strength is determined by superposition of the fault mode field strength determined in the substep 1 and the substep 2 and the unit maintenance difficulty, and the unit fault field strength is in direct proportion to the fault mode field strength and in inverse proportion to the unit maintenance difficulty.
Step three: and calculating the surface fault field intensity of the product.
The surface fault field intensity is formed by superposing the fault radiation values of the space fault field intensity of the unit composed of partial products on the surface of the product.
This step comprises 4 sub-steps:
step 1: the method based on ZL 201410778944.1 'product assembly fault visualization method based on 3D digital model' step one is used for converting irregular products into regular three-dimensional rectangular parallelepiped wire frame models.
Step 2: and converting the product composition units into three-dimensional cylinders by using a minimum containment principle, further determining the center of gravity, the radius of the bottom surface, the height of the cylinders and the central axial direction of the cylinders, and determining the fault field strength of the cylinders according to the fault field strength of the unit space.
(1) Establishing a three-dimensional Cartesian coordinate system D along three directions of the length, the width and the height of the cuboid respectively by taking the gravity center of the product as an origin O, and recording the three-dimensional Cartesian coordinate system D as (X, Y and Z);
(2) establishing a three-dimensional sub-coordinate system D along the directions of the X axis, the Y axis and the Z axis of the coordinate system D by taking the gravity center of the unit as an origin o, and recording the three-dimensional sub-coordinate system D as (X, Y, Z);
(3) constructing cylinders by using the unit gravity center as the gravity center of a three-dimensional cylinder and using an x axis, a y axis and a z axis as central axes respectively by using a minimum inclusion principle, recording the cylinders as Cx, Cy and Cz, comparing the volumes of the three cylinders, taking the cylinder with the minimum volume as the three-dimensional cylinder corresponding to a product unit, recording the cylinder as C | k (k is x, y and z), recording the radius of the cylinder as r, and recording the height as HC。
Note: and k is x, the volume of the cylinder constructed by taking the x axis as the central axis is minimum, and the like.
(4) And assigning the unit space fault field intensity to the corresponding cylinder C | k, namely the fault field intensity of the cylinder C | k is equal to the unit space fault field intensity of the corresponding product.
And step 3: the projected area of the cylinder on the surface of the product is calculated.
The projection direction is specified as follows:
(1) the central cross section S of the cylinder (S is a cross section which is made by taking the center of gravity of the cylinder as the center of a circle and is vertical to the k axis of the central shaft, namely the circle with the center of a circle as the center of the cylinder and the radius of r): and directly projecting the projection image to the surface of the product along the positive and negative directions of the k axis, wherein the projection is a cross section projection area.
(2) Cylinder side: with a section (length H) of the central axis of the cylinderCA rectangle of width 2 r) projected onto the surface of the product along the radius of the cross-section S, i.e. 360 deg. onto the surface of the product. When the radiation is radiated to the surface of a product, the projection area of the radiation is to deduct the area which cannot be projected, such as windows, cabin doors and the like of civil aircrafts.
And 4, step 4: the radiation field of the unit to the surface of the product is calculated.
(1) Radiation field of the central cross section S of the cylinder: first, the center O of the cross section S is calculatedDThe absolute distance of the projection plane in the positive and negative directions along the k-axis is denoted as d+、d-(ii) a Then, the radiation fields of the cross section S in the positive and negative directions are calculated, and are in direct proportion to the unit space fault field strength and in inverse proportion to the absolute distance.
(2) Radiation field at the side of the cylinder: firstly, calculating the distance from the center of gravity of the cylinder to the surface of the product along the radius direction of the cross section S, setting an angle epsilon (epsilon can be divided by 360, and epsilon needs to be large enough to ensure that the same surface cannot be repeatedly projected by the same side), calculating the distance from the center of gravity of the cylinder to the surface of the product along the radius direction of the cross section S once the radius of the cross section S rotates epsilon DEG along the cross section, and thus obtaining a distance array
Figure BDA0002428236370000031
Then, calculating the radiation field of the fault field intensity of the cylinder on the surface of the product, wherein the radiation field is proportional to the fault field intensity of the cylinder and is proportional to diIn inverse proportion.
And 5: and calculating the surface fault field intensity of the product.
Because the product constitutional units are numerous, the space fault field intensity of each constitutional unit projects the product surface and forms the radiation field, still need further stack calculation product surface fault field intensity, and then provide the basis for product maintenance flap design.
(1) Taking any point f (f is 1,2, …) on the surface of the productN) calculating the sum of all radiation values projected to the point
Figure BDA0002428236370000032
(2) Normalizing to determine the fault field strength of the surface point f (f is 1,2, …, n) of the product
Figure BDA0002428236370000033
(3) Intensity of fault field
Figure BDA0002428236370000034
Compare with trouble field intensity colour strip, get the colour value that the trouble field intensity of point f ( f 1,2, …, n) corresponds on the product surface, color the product corresponding position to obtain product surface trouble field intensity distribution.
And coloring the product based on the steps from the first step to the third step, and further obtaining the field intensity distribution of the surface fault of the product. Based on this distribution, the designer can further proceed with the maintenance flap design.
Drawings
FIG. 1 is a flow chart of the method
FIG. 2 product three-dimensional cuboid wireframe model example (a) product (b) cuboid wireframe
FIG. 3 Cartesian coordinate system example based on a three-dimensional cuboid wire-frame model of a product
FIG. 4 three-dimensional sub-coordinate system example of a cell
FIG. 5 example of a minimal containment cylinder C | k
FIG. 6 is a schematic diagram showing an example of the projection area of the cross section S of the cylinder in the positive and negative directions of the x-axis
FIG. 7 projection area of cylinder side on product surface example (a) ε ° projection area (b)360 ° projection area
FIG. 8 Fault field intensity color Bar
FIG. 9 product surface fault field profile
Detailed Description
The process flow of the method of the invention is shown in figure 1. For a better understanding of the features and advantages of the present invention, reference is made to the following detailed description taken in conjunction with the accompanying drawings and examples. The case chosen by the present invention is a product P comprising 3 component units. The specific implementation steps are as follows:
the method comprises the following steps: and calculating the risk index of each unit and each failure mode of the product.
And calculating the risk index of each component unit and each fault mode of the product according to the result of the fault mode influence and hazard analysis (FMECA) of the product, wherein the risk index is determined by the occurrence probability level, the severity level and the detection difficulty level of the fault mode.
The FMECA results of the product can be represented by table 1, from which the occurrence probability level, severity level, and detection difficulty level of each unit and each failure mode can be obtained, and further the risk index RPN can be calculated. The calculation formula for RPN is as follows:
TABLE 1 FMECA results presentation for the product
Figure BDA0002428236370000041
Note: in the GJB/1391, the value ranges defining the occurrence probability level, the severity level, and the detection difficulty level are {1,2,3, …,10 }.
RPN＝ESR*OPR*DDR (1)
Wherein ESR represents a severity level, OPR represents an occurrence probability level, and DDR represents a detection difficulty level.
FMECA results for case product P are shown in table 2.
Table 2 FMECA results for product P
Figure BDA0002428236370000042
Step two: and calculating the spatial fault field intensity of the product composition unit.
The space fault field intensity is a quantitative index for comprehensively describing the fault mode risk index and the maintenance difficulty of the unit. The cell space fault field intensity is superposed by the fault field intensity of the cell fault mode. This step comprises 3 sub-steps:
step 1: and calculating the fault field intensity of each fault mode in the product composition unit i. It is determined by the risk index for each failure mode. The higher the risk index, the more serious the fault consequence and the higher the fault field strength. The calculation formula of the fault field intensity of the fault mode is as follows:
Figure BDA0002428236370000051
wherein the content of the first and second substances,
Figure BDA0002428236370000052
denoted as cell i failure mode FMijFault field strength, RPNijIs a risk index for failure modes.
Table 3 shows the calculation results of the failure mode failure field strength of the case product P.
TABLE 3 failure mode failure field strength of product P
Unit name Failure mode Severity rating Degree of probability of occurrence Detecting difficulty level Risk index Field strength at fault
Unit
1 FM11 5 4 9 180 0.18
Unit 1 FM12 6 4 2 48 0.048
Unit 1 FM13 6 4 4 96 0.096
Unit 1 FM14 8 1 1 8 0.008
Unit 2 FM21 2 8 1 16 0.016
Unit 2 FM22 6 6 6 216 0.216
Unit 2 FM23 5 4 5 100 0.1
Unit 3 FM31 2 8 9 144 0.144
Unit 3 FM32 1 7 6 42 0.042
Unit 3 FM33 8 6 8 384 0.384
Unit 3 FM34 4 6 2 48 0.048
Unit 3 FM35 8 8 8 512 0.512
Step 2: and calculating the maintenance difficulty of each product composition unit i. For a product component, the difficulty of repair can be measured by accessibility and detachability. The better the accessibility, the lower the maintenance difficulty; the better the detachability, the lower the difficulty of maintenance.
Maintenance difficulty MD of unit iiThe specific definition is as follows:
Figure BDA0002428236370000053
wherein, REDiIs the achievable difficulty rating, RMD, of cell iiIs the removable difficulty rating of unit i. Specific scoring criteria are shown in tables 4 and 5.
TABLE 4 Unit achievable difficulty level definition
Figure BDA0002428236370000054
TABLE 5 Unit Detachables difficulty rating Definitions
Figure BDA0002428236370000055
Figure BDA0002428236370000061
Table 6 shows the calculation results of the failure mode failure field strength of the case product P.
TABLE 6 maintenance difficulty of product P
Unit name Can reach the difficulty level Detachable difficulty rating Difficulty of maintenance
Unit
1 Extremely difficult (10) Relatively difficult (8) 0.80
Unit 2 In general (6) Relatively difficult (8) 0.48
Unit 3 Relatively easy (4) In general (6) 0.24
And step 3: and calculating the spatial fault field intensity of each product composition unit i. The unit space fault field strength is determined by superposition of the fault mode field strength determined in the substep 1 and the substep 2 and the unit maintenance difficulty, and the unit fault field strength is in direct proportion to the fault mode field strength and in inverse proportion to the unit maintenance difficulty. The calculation formula is as follows:
Figure BDA0002428236370000062
wherein the content of the first and second substances,
Figure BDA0002428236370000063
indicating the field strength of the failure of cell i, JiRepresenting the total number of failure modes for cell i.
Table 7 shows the calculation results of the failure mode failure field strength of the case product P.
TABLE 7 field strength of each unit failure of product P
Unit name Sum of failure mode field strengths Difficulty of maintenance Field strength at fault
Unit
1 0.332 0.80 0.4150
Unit 2 0.332 0.48 0.6917
Unit 3 1.13 0.24 4.7083
Step three: and calculating the surface fault field intensity of the product. The surface fault field intensity is formed by superposing the fault radiation values of the space fault field intensity of the unit composed of partial products on the surface of the product. This step comprises 4 sub-steps:
step 1: the method based on ZL 201410778944.1 'product assembly fault visualization method based on 3D digital model' step one is used for converting irregular products into regular three-dimensional rectangular parallelepiped wire frame models.
An exemplary graph is shown in fig. 2.
Step 2: and (3) converting the product composition unit i into a three-dimensional cylinder by using a minimum containment principle, further determining the center of gravity, the radius of the bottom surface, the height of the cylinder and the central axial direction of the cylinder, and determining the fault field strength of the cylinder according to the fault field strength of the unit space.
(1) And (3) establishing a three-dimensional Cartesian coordinate system D along three directions of the length, the width and the height of the cuboid respectively by taking the gravity center of the product as an origin O, and recording the three-dimensional Cartesian coordinate system D as (X, Y and Z).
An exemplary graph is shown in fig. 3.
(2) And (3) establishing a three-dimensional sub-coordinate system D along the directions of the X axis, the Y axis and the Z axis of the coordinate system D by taking the gravity center of the unit i as an origin o, and recording the three-dimensional sub-coordinate system D as (X, Y, Z).
An exemplary graph is shown in fig. 4.
(3) By using the principle of minimum containment, the gravity center of the unit i is taken as the gravity center of a three-dimensional cylinder, and the x axis, the y axis and the z axis are taken as central axes respectivelyConstructing cylinders, recording the cylinder as Cx, Cy and Cz, comparing the volumes of the three cylinders, taking the cylinder with the smallest volume as the three-dimensional cylinder corresponding to the product unit, recording the cylinder as C | k (k ═ x, y and z), recording the radius of the cylinder as r and the height as HC。
Note: and k is x, the volume of the cylinder constructed by taking the x axis as the central axis is minimum, and the like.
An example of a minimum-containment cylinder C | k is shown in fig. 5, where k ═ x.
(4) And assigning the unit space fault field intensity to a cylinder C | k corresponding to the unit i, namely the fault field intensity of the cylinder C | k is equal to the space fault field intensity of the unit i.
And step 3: the projected area of the cylinder of cell i on the surface of the product is calculated. The projection direction is specified as follows:
(1) the central cross section S of the cylinder (S is a cross section which is made by taking the center of gravity of the cylinder as the center of a circle and is vertical to the k axis of the central shaft, namely the circle with the center of a circle as the center of the cylinder and the radius of r): and directly projecting the projection image to a surface along the positive and negative directions of the k axis, wherein the projection is a cross section projection area.
An example graph is shown in fig. 6.
(2) Cylinder side: with a section (length H) of the central axis of the cylinderCA rectangle of width 2 r) projected onto the surface of the product along the radius of the cross-section S, i.e. 360 deg. onto the surface of the product. When the radiation is radiated to the surface of a product, the projection area of the radiation is to deduct the area which cannot be projected, such as windows, cabin doors and the like of civil aircrafts.
An exemplary graph is shown in fig. 7.
And 4, step 4: the radiation field of the unit i to the surface of the product is calculated.
(1) Radiation field of the central cross section S of the cylinder: first, the center O of the cross section S is calculatedDThe absolute distance of the projection plane in the positive and negative directions along the k-axis is recorded as
Figure BDA0002428236370000071
Then, the radiation fields of the cross section S in the positive and negative directions are calculated, and are in direct proportion to the unit space fault field strength and in inverse proportion to the absolute distance.
SquareTo the radiation field
Figure BDA0002428236370000072
The calculation formula of (a) is as follows:
Figure BDA0002428236370000081
wherein the content of the first and second substances,
Figure BDA0002428236370000082
indicating the strength of the failed field of the cell i,
Figure BDA0002428236370000083
the center O of the cross section S of the cell iDAbsolute distance of the projection plane in the positive direction of the k-axis.
Negative direction radiation field
Figure BDA0002428236370000084
The calculation formula of (a) is as follows:
Figure BDA0002428236370000085
wherein the content of the first and second substances,
Figure BDA0002428236370000086
the center O of the cross section S of the cell iDAbsolute distance of the plane of projection along the negative k-axis direction.
(2) Radiation field at the side of the cylinder: first, the distance from the center of gravity of the cylinder of unit i to the surface of the product along the radial direction of the cross section S is calculated, and an angle ε can be seti(εiCan be divided by 360 and epsiloniLarge enough to ensure that the same surface is not repeatedly projected by the same side), calculating the distance from the center of gravity of the cylinder to the surface of the product along the radial direction of the cross section S every time the radius of the cross section S rotates by epsilon DEG along the cross section, thereby obtaining a distance array
Figure BDA0002428236370000087
Then, calculating the radiation field of the fault field intensity on the side surface of the cylinder on the surface of the product, wherein the radiation field is proportional to the fault field intensity of the cylinder and is proportional to dieIn inverse proportion.
(εiX e) ° direction radiation field calculation formula is as follows:
Figure BDA0002428236370000088
wherein the content of the first and second substances,
Figure BDA0002428236370000089
the cylinder side representing unit i is at (. epsilon.)iX e) radiation field in the direction; dieRepresents the center edge (ε) of the center axis cross section of the cell iiAe) distance from the surface of the product.
And 5: and calculating the surface fault field intensity of the product.
Because the product constitutional units are numerous, the space fault field intensity of each constitutional unit projects the product surface and forms the radiation field, still need further stack calculation surface fault field intensity, and then provide the basis for product maintenance flap design.
(1) Taking any point f (f is 1,2, …, n) on the surface of the product, and calculating the sum of all the radiation values projected to the point
Figure BDA00024282363700000810
The formula is as follows:
Figure BDA00024282363700000811
wherein, IfA set of elements representing a point having a radiation field at the surface f of the product; mu.s i1 represents that the cross section S of the unit i has a radiation field at the point f along the positive direction of the k axis and has no radiation field at the point f along the negative direction of the k axis; mu.si0 denotes that the cross section S of the element i has no radiation field at point f in the positive k-axis direction and has a radiation field at point f in the negative k-axis direction
(2) Further performing normalization to determineField strength at fault at point f (f ═ 1,2, …, n) on the surface of a product
Figure BDA0002428236370000093
The processing formula is as follows:
Figure BDA0002428236370000091
(3) intensity of fault field
Figure BDA0002428236370000092
And comparing the color value corresponding to the fault field intensity of a product surface point f (f is 1,2, …, n) with a fault field intensity color bar (see fig. 8), and coloring the projection area on the product surface.
Based on the steps from the first step to the third step, the surface of the product can be colored, and a field intensity distribution diagram of the surface fault of the product is obtained, as shown in fig. 9. Based on this distribution, the designer can further proceed with the maintenance flap design. As shown in fig. 9, the field strength of the fault in the left and right central regions a1 and a2 is much higher than that in the surrounding regions, so that a maintenance flap needs to be designed in each of a1 and a 2.

Claims (1)

1. A method for constructing a space fault field model based on a three-dimensional model of a product is characterized by comprising the following steps:
the method comprises the following steps: calculating the risk index of each unit and each failure mode of the product;
according to the FMECA result of the product fault mode influence and hazard analysis, calculating the risk index of each component unit and each fault mode of the product, wherein the risk index is determined by the fault mode occurrence probability level, the severity level and the detection difficulty level;
step two: calculating the spatial fault field intensity of the product composition unit;
the space fault field intensity is a quantitative index for comprehensively describing the unit fault mode risk index and the maintenance difficulty, wherein the unit space fault field intensity is superposed by the fault field intensity of the unit fault mode, and the step comprises 3 sub-steps:
step 1: calculating the fault field strength of each fault mode in the product composition unit, wherein the fault field strength is determined by the risk index of each fault mode;
step 2: calculating a repair difficulty for each product component, the repair difficulty being measurable by accessibility and detachability for the product component: the better the accessibility, the lower the maintenance difficulty; the better the detachability, the lower the maintenance difficulty;
and step 3: calculating the space fault field intensity of each product composition unit, wherein the space fault field intensity of each unit is determined by the superposition of the fault mode field intensity and the unit maintenance difficulty determined in the substep 1 and the substep 2, and the unit fault field intensity is in direct proportion to the fault mode field intensity and in inverse proportion to the unit maintenance difficulty;
step three: calculating the surface fault field intensity of the product;
the surface fault field intensity is formed by superposing fault radiation values of partial product composition unit space fault field intensities on the surface of a product, and the step comprises 5 sub-steps:
step 1: converting an irregular three-dimensional physical model of a product into a regular three-dimensional rectangular wire frame model by using a minimum containment principle, wherein the length, the width and the height of the regular three-dimensional rectangular wire frame model are respectively represented by L, W, H and are marked as (L, W and H);
step 2: continuously applying a minimum containment principle to convert product composition units into three-dimensional cylinders, further determining the center of gravity, the radius of the bottom surface, the height of the cylinders and the central axial direction of the cylinders, and determining the fault field intensity of the cylinders according to the fault field intensity of the unit space;
(1) establishing a three-dimensional Cartesian coordinate system D along three directions of length, width and height of a cuboid (L, W and H) by taking the gravity center of the product as an origin O, and recording the three-dimensional Cartesian coordinate system D as (X, Y and Z);
(2) establishing a three-dimensional sub-coordinate system D along the directions of the X axis, the Y axis and the Z axis of the coordinate system D by taking the gravity center of the unit as an origin o, and recording the three-dimensional sub-coordinate system D as (X, Y, Z);
(3) constructing cylinders by using the principle of minimum containment, taking the center of gravity of a unit as the center of gravity of a three-dimensional cylinder, respectively taking an x axis, a y axis and a z axis as central axes, recording the cylinders as Cx, Cy and Cz, comparing the volumes of the three cylinders, and taking the cylinder with the minimum volume as a corresponding product unitThree-dimensional cylinder, denoted C-k(k ═ x, y, z), the cylinder radius is denoted r and the height is denoted HC；
Wherein, k is x to represent that the volume of a cylinder constructed by taking the x axis as a central axis is minimum, and so on;
(4) assigning the unit space fault field intensity to the corresponding cylinder CkI.e. cylinder C-kThe fault field intensity of the corresponding product unit space is equal to the fault field intensity of the corresponding product unit space;
and step 3: calculating a projection area of the cylinder on the surface of the product;
the projection direction is specified as follows:
(1) cylinder center cross section S: s is a cross section which is made by taking the center of gravity of a cylinder as the center of a circle and is vertical to a k axis of a central shaft, namely a circle with the center of a circle as the center of the cylinder and a radius of r, and the cross section is directly projected on the surface of a product along the positive and negative directions of the k axis, wherein the projection is a cross section projection area;
(2) cylinder side: one length is HCThe central axis section of the rectangular cylinder with the width of 2r is projected to the surface of a product along the radius direction of the cross section S, namely projected to the surface of the product at 360 degrees, and when the central axis section of the rectangular cylinder is radiated to the surface of the product, the projection area of the central axis section is deducted from the area which cannot be projected;
and 4, step 4: calculating the radiation field of the unit to the surface of the product;
(1) radiation field of the central cross section S of the cylinder: first, the center O of the cross section S is calculatedDThe absolute distance of the projection plane in the positive and negative directions along the k-axis is denoted as d+、d-(ii) a Then, calculating radiation fields of the cross section S in the positive direction and the negative direction respectively, wherein the radiation fields are in direct proportion to the fault field strength of the unit space and in inverse proportion to the absolute distance;
(2) radiation field at the side of the cylinder: firstly, calculating the distance from the center of gravity of the cylinder to the surface of the product along the radial direction of a cross section S, setting an angle epsilon, wherein epsilon can be divided by 360, epsilon needs to be large enough to ensure that the same surface can not be projected by the same side repeatedly, and calculating the distance from the center of gravity of the cylinder to the surface of the product along the radial direction of the cross section S once every time the radius of the cross section S rotates epsilon along the cross section, thereby obtaining a distance array
Figure FDA0002944491560000021
Then, calculating the radiation field of the fault field intensity of the cylinder on the surface of the product, wherein the radiation field is proportional to the fault field intensity of the cylinder and is proportional to diIn inverse proportion;
and 5: calculating the surface fault field intensity of the product;
because the product constitutional unit is numerous, the space fault field intensity of each constitutional unit projects the product surface and forms the radiation field, still need further stack calculation product surface fault field intensity, and then provides the basis for product maintenance flap design, and its process is as follows:
(1) taking any point f on the surface of the product, wherein f is 1,2, …, n, and calculating the sum of all the radiation values projected to the point
Figure FDA0002944491560000022
(2) Normalization processing is carried out to determine the fault field intensity of the surface point f of the product
Figure FDA0002944491560000023
Wherein f is 1,2, …, n;
(3) intensity of fault field
Figure FDA0002944491560000024
Compare with trouble field intensity colour strip, get the colour value that the trouble field intensity of point f corresponds on the product surface, wherein f 1,2, …, n, correspond the position to the product and colour to obtain product surface trouble field intensity distribution.
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