CN111539136A - Surface topography construction method based on measurement data - Google Patents

Surface topography construction method based on measurement data Download PDF

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CN111539136A
CN111539136A CN202010204193.8A CN202010204193A CN111539136A CN 111539136 A CN111539136 A CN 111539136A CN 202010204193 A CN202010204193 A CN 202010204193A CN 111539136 A CN111539136 A CN 111539136A
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CN111539136B (en
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徐戊矫
刘承尚
刘旻瑶
牛天昊
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Chongqing University
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Abstract

The invention discloses a surface topography construction method based on experimental measurement data, which comprises the following steps: 1) scanning the appearance of the surface of the product to obtain an actual measurement matrix S of the rough surface; 2) carrying out dimension transformation on the matrix S to generate a point cloud matrix P of a rough surfaces(ii) a 3) Constructing a finite element model of a product to generate a three-dimensional finite element model M with a smooth surface; 4) extracting all node information of the model M to form a point cloud matrix P of the modelm(ii) a 5) Calculating two groups of point cloud matrixes PmAnd PsA weight matrix W of; 6) according to the weight matrix W, a point cloud matrix P of the model is obtainedmIs transformed to form a new point cloud matrix Pm *(ii) a 7) Updating the nodes of the finite element model M into a point cloud matrix Pm *Outputting a finite element model M of the actually measured rough surface*. The method of the invention analyzes the acoustic optical property of the rough surface to the product and the antifriction and antiwear propertiesThe influence of performance has greatly improved product analysis's efficiency and quality, and the step is simple, and it is convenient to use.

Description

Surface topography construction method based on measurement data
Technical Field
The invention relates to the field of surface topography construction, in particular to a surface topography construction method based on experimental measurement data.
Background
Strictly speaking, all product surfaces do not present a completely smooth surface, and various process-related asperities are present on the surface of the product. The existence of the surface roughness has important influence on the acoustic optical performance and the friction-reducing and wear-resisting performance of the product. For a rough surface, the rough surface is usually considered on a smooth surface basis in order to make the model of the product more accurate in finite element analysis.
At present, the generation method of the rough surface model is mainly to construct a model similar to actual measurement data, so that the two models have the same characteristic parameters in the statistical sense. Such as gaussian surface models, non-gaussian surface models, fractal surface models, and the like. However, the actual rough morphology is very complex, the analytic solution of the rough morphology is difficult to find by using a mathematical model, and the problem of poor precision exists by using a similar model. And the rough morphology varies, the characteristic parameters can be the same in the statistical sense by using similar models, but the detailed information of the rough morphology can be lost.
The most accurate method is not to use a similar model, but to directly use the measured data as the surface topography of the model. Therefore, it is very important to develop a method of constructing a surface topography that directly uses the measured asperity as a model.
Disclosure of Invention
The invention aims to provide a surface morphology construction method which can solve the problems of poor precision of using a similar model, loss of morphology detail information and the like in a rough surface finite element model construction process.
The technical scheme adopted for achieving the aim of the invention is that the surface topography construction method based on the measured data is used for constructing the surface topography of a finite element model by using rough surface data obtained by measurement, and comprises the following steps:
1) scanning the appearance of the surface of the product to obtain an actual measurement matrix S of the rough surface;
2) carrying out dimension transformation on the matrix S to generate a point cloud matrix P of a rough surfaces；
3) Constructing a finite element model of the product to generate a three-dimensional finite element model M with a smooth surface;
4) extracting all node information of the model M to form a point cloud matrix P of the model Mm；
5) Calculating the point cloud matrix PmAnd a point cloud matrix PsA weight matrix W of;
6) according to the weight matrix W, carrying out three-dimensional point cloud P on the model MmIs transformed to form a new point cloud matrix Pm *；
7) Updating the nodes of the model M into a point cloud matrix Pm *Outputting a finite element model M of the actually measured rough surface*。
Further, the calculation of the weight matrix W in step 5) includes the following steps:
5-1) Point cloud matrix P of the model MmIs denoted as Pm＝{Pm1(xm1，ym1，zm1)，…，Pmi(xmi，ymi，zmi)，…，PmU(xmU，ymU，zmU) Where U is the point cloud matrix PmThe total number of coordinate points of (a); the point cloud matrix PsIs denoted as Ps＝{Ps1(xs1，ys1，zs1)，…，Psj(xsj，ysj，zsj)，…，PsV(xsV，ysV，zsV) Where V is the point cloud matrix PsThe total number of coordinate points of (a);
for the point cloud matrix PmAny point P ofmi(xmi，ymi，zmi) First, the point and point cloud matrix P is obtainedsDistance matrix D of all pointsmi＝{Dmi-s1，Dmi-s2，…，Dmi-sj，…，Dmi-sVAnd (c) the step of (c) in which,
Figure BDA0002420413460000021
5-2) combining the distance matrix DmiThe first four values are taken after being arranged according to the sequence from small to big, namely the separation point Pmi(xmi，ymi，zmi) The four nearest distances are denoted as Dmi1、Dmi2、Dmi3And Dmi4The four distances correspond to a point cloud matrix PsFour points in the interior are marked as Psi1、Psi2、Psi3And Psi4(ii) a The sum of the four distances is DmiAnd then:
Dmi＝Dmi1+Dmi2+Dmi3+Dmi4(2)
5-3) points P are respectively assignedsi1、Psi2、Psi3And Psi4Different weights, the relationship between the assigned weight value and the distance value of the corresponding point is as follows:
Figure BDA0002420413460000022
Figure BDA0002420413460000023
Figure BDA0002420413460000024
Figure BDA0002420413460000025
wherein, ω ismi1Is a point Psi1Weight value of, ωmi2Is a point Psi2Weight value of, ωmi3Is a point Psi3Weight value of, ωmi4Is a point Psi4The weight value of (1);
5-4) combining all weight coefficients to form a weight matrix W, i.e.
Figure BDA0002420413460000026
The technical effect of the method is needless to say that the data of actually measured rough topography is directly used for constructing the surface topography of the finite element model. Compared with a similar model, the actual model constructed by the method is more accurate, and the detailed information of the surface morphology is not lost. The method is suitable for considering the rough morphology during finite element analysis of the product and analyzing the influence of the rough surface on the acoustic optical performance and the antifriction and antiwear performance of the product. The method greatly improves the efficiency and quality of product analysis; meanwhile, the method has simple steps, and the user can be trained to operate on duty simply, so the method is convenient and fast to use.
Drawings
FIG. 1 is a flow chart of the operation of the method of the present invention;
FIG. 2 is a graph of rough topography data obtained from actual measurements of a product location A;
FIG. 3 is a smooth planar model used in finite element analysis of a product;
FIG. 4 is a model of the rough surface actually measured at product site A;
FIG. 5 is a rough topography data obtained from actual measurements of product site B;
fig. 6 is a model of the rough surface actually measured at product site B.
Detailed Description
The present invention is further illustrated by the following examples, but it should not be construed that the scope of the above-described subject matter is limited to the following examples. Various substitutions and alterations can be made without departing from the technical idea of the invention and the scope of the invention is covered by the present invention according to the common technical knowledge and the conventional means in the field.
Example 1:
the embodiment discloses a surface topography construction method based on measurement data aiming at rough topography data obtained by actually scanning the surface of a product, and the method is a surface topography construction flow chart and mainly comprises the following steps of:
1) referring to a diagram a in fig. 2, the surface of a product part a is scanned for topography, and an actual measurement matrix S of the rough topography is obtained as input; the matrix S contains all height information from the light source point to the surface of the product in the scanning process, and the horizontal and vertical coordinates of the matrix S are pixel information instead of distance information.
2) Carrying out dimension transformation on an actual measurement matrix S of the rough topography, transforming pixel information of horizontal and vertical coordinates of the matrix into distance information, and generating a point cloud matrix P of the rough surfacesSee panel b in fig. 2.
3) And constructing a finite element model of the product to generate a three-dimensional finite element model M with a smooth surface. In order to ensure that the model has higher computational accuracy on the surface, the surface mesh of the model needs to be refined, such as a diagram a in fig. 3.
4) Extracting all node information of the model M to form a point cloud matrix P of the modelmAs shown in diagram b of fig. 3.
5) Calculating two groups of point cloud matrixes PmAnd PsA weight matrix W of; wherein, two groups of point cloud matrixes PmAnd PsThe calculation of the weight matrix W of (a) comprises the steps of:
5-1) ordering the point cloud matrix P of the finite element modelmHas the coordinate of Pm＝{Pm1(xm1，ym1，zm1)，…，Pmi(xmi，ymi，zmi)，…，PmU(xmU，ymU，zmU) Where U is the point cloud matrix PmThe total number of coordinate points. Let point cloud matrix PsHas the coordinate of Ps＝{Ps1(xs1，ys1，zs1)，…，Psj(xsj，ysj，zsj)，…，PsV(xsV，ysV，zsV) Where V is the point cloud matrix PsThe total number of coordinate points.
To point cloud matrix PmAny point P ofmi(xmi，ymi，zmi) First, it and the point cloud matrix P are obtainedsDistance matrix D of all pointsmi＝{Dmi-s1，Dmi-s2，…，Dmi-sj，…，Dmi-sVAnd (c) the step of (c) in which,
Figure BDA0002420413460000041
5-2) distance matrix DmiThe first four values are taken after being arranged according to the sequence from small to big, namely the separation point Pmi(xmi，ymi，zmi) The four nearest distances are denoted as Dmi1，Dmi2，Dmi3And Dmi4. They correspond to the point cloud matrix PsThe four points are marked as Psi1，Psi2，Psi3And Psi4. Let the sum of these four distances be DmiAnd satisfies the following conditions:
Dmi＝Dmi1+Dmi2+Dmi3+Dmi4(2)
5-3) next, respectively assigning different weights to the four points, wherein the weight values are related to the distance values of the four points. The smaller the distance, the greater the weight, and the weight is related to the distance as follows:
Figure BDA0002420413460000042
Figure BDA0002420413460000043
Figure BDA0002420413460000044
Figure BDA0002420413460000045
wherein, ω ismi1Is a point Psi1Weight value of, ωmi2Is a point Psi2Weight value of, ωmi3Is a point Psi3Weight value of, ωmi4Is a point Psi4The weight value of (1);
5-4) combining all weight coefficients to form a weight matrix W, i.e.
Figure BDA0002420413460000046
6) According to the weight matrix W, a point cloud matrix P of the model is obtainedmIs transformed to form a new point cloud matrix Pm *As shown in fig. 4 a.
7) Updating the nodes of the finite element model M into a point cloud matrix Pm *Outputting a finite element model M of the actually measured rough surface*As shown in fig. 4 b.
The finite element model M of the rough surface of the actual measurement of the product part A is obtained through the above steps*The model can be further used for analyzing the influence of the rough surface on the acoustic optical performance and the friction-reducing and wear-resisting performance of the product. The actual model constructed by the method is more accurate, and the detailed information of the surface morphology is not lost. Meanwhile, the method has simple steps, and greatly improves the efficiency and quality of product analysis.
Example 2:
the embodiment discloses a surface topography construction method based on measurement data, which directly uses the data of actually measured rough topography for surface topography construction of a finite element model, and mainly comprises the following steps:
1) and (3) carrying out topography scanning on the surface of the product part B to obtain an actual measurement matrix S of the rough surface, such as a graph a in figure 5.
2) Carrying out dimension transformation on the matrix S to generate a point cloud matrix P of a rough surfacesAs shown in fig. 5 b.
3) And constructing a finite element model of the product to generate a three-dimensional finite element model M with a smooth surface.
4) Extracting all node information of the model M to form a point cloud matrix P of the modelm。
5) Calculating two groups of point cloud matrixes PmAnd PsThe weight matrix W.
6) According to the weight matrix W, a point cloud matrix P of the model is obtainedmIs transformed to form a new point cloud matrix Pm *E.g. a in FIG. 6Figure (a).
7) Updating the nodes of the finite element model M into a point cloud matrix Pm *Outputting a finite element model M of the actually measured rough surface*As shown in fig. 6 b.
In this example, a finite element model M of the actual measured rough surface of the product site B was obtained*The model can be further used for analyzing the influence of the rough surface on the acoustic optical performance and the friction-reducing and wear-resisting performance of the product. The actual model constructed by the method is more accurate, and the detailed information of the surface morphology is not lost. Meanwhile, the method has simple steps, and greatly improves the efficiency and quality of product analysis.

Claims (2)

1. A surface topography construction method based on measurement data is characterized in that: carrying out surface topography construction of a finite element model on rough surface data obtained by measurement, and comprising the following steps:
1) scanning the appearance of the surface of the product to obtain an actual measurement matrix S of the rough surface;
2) carrying out dimension transformation on the matrix S to generate a point cloud matrix P of a rough surfaces；
3) Constructing a finite element model of the product to generate a three-dimensional finite element model M with a smooth surface;
4) extracting all node information of the model M to form a point cloud matrix P of the model Mm；
5) Calculating the point cloud matrix PmAnd a point cloud matrix PsA weight matrix W of;
6) according to the weight matrix W, carrying out three-dimensional point cloud P on the model MmIs transformed to form a new point cloud matrix Pm *；
7) Updating the nodes of the model M into a point cloud matrix Pm *Outputting a finite element model M of the actually measured rough surface*。
2. The method for constructing surface topography based on measurement data according to claim 1, wherein: the calculation of the weight matrix W in the step 5) comprises the following steps:
5-1) Point cloud matrix P of the model MmIs denoted as Pm＝{Pm1(xm1,ym1,zm1),…,Pmi(xmi,ymi,zmi),…,PmU(xmU,ymU,zmU) Where U is the point cloud matrix PmThe total number of coordinate points of (a); the point cloud matrix PsIs denoted as Ps＝{Ps1(xs1,ys1,zs1),…,Psj(xsj,ysj,zsj),…,PsV(xsV,ysV,zsV) Where V is the point cloud matrix PsThe total number of coordinate points of (a);
for the point cloud matrix PmAny point P ofmi(xmi,ymi,zmi) First, the point and point cloud matrix P is obtainedsDistance matrix D of all pointsmi＝{Dmi-s1,Dmi-s2,…,Dmi-sj,…,Dmi-sVAnd (c) the step of (c) in which,
Figure FDA0002420413450000011
5-2) combining the distance matrix DmiThe first four values are taken after being arranged according to the sequence from small to big, namely the separation point Pmi(xmi,ymi,zmi) The four nearest distances are denoted as Dmi1、Dmi2、Dmi3And Dmi4The four distances correspond to a point cloud matrix PsFour points in the interior are marked as Psi1、Psi2、Psi3And Psi4(ii) a The sum of the four distances is DmiAnd then:
Dmi＝Dmi1+Dmi2+Dmi3+Dmi4(2)
5-3) points P are respectively assignedsi1、Psi2、Psi3And Psi4Different weights, the relation between the assigned weight value and the distance value of the corresponding pointThe following were used:
Figure FDA0002420413450000012
Figure FDA0002420413450000013
Figure FDA0002420413450000014
Figure FDA0002420413450000021
wherein, ω ismi1Is a point Psi1Weight value of, ωmi2Is a point Psi2Weight value of, ωmi3Is a point Psi3Weight value of, ωmi4Is a point Psi4The weight value of (1);
5-4) combining all weight coefficients to form a weight matrix W, i.e.
Figure FDA0002420413450000022
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