CN109900704B - In-situ three-dimensional reconstruction method for microscopic morphology of worn surface of gear - Google Patents
In-situ three-dimensional reconstruction method for microscopic morphology of worn surface of gear Download PDFInfo
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Abstract
In the in-situ three-dimensional reconstruction method of the gear wear surface micro-topography, a set of embedded digital microscopic image acquisition system comprising 8 point light sources is adopted to obtain 8 microscopic images under different illumination angles, a near-field point light source illumination model is established after environment setting and system calibration are carried out, and the spatial position of the light source and an attenuation model are calibrated; then, combining two methods of estimating the normal direction from the multi-image constraint and recovering the surface shape from the normal direction, and calculating to obtain a primary reconstruction surface; processing the preliminary reconstruction information by using a polynomial fitting, color reduction and projection conversion algorithm to obtain the micro-morphology of the surface of the gear; finally, carrying out statistical calculation on the height information to obtain the appearance characteristics of the worn surface of the gear; the method is convenient to carry and operate, can obtain the three-dimensional appearance and surface characteristics of the worn surface of the gear, and has important significance for accurate analysis of the process wear evolution of the gear friction pair and visual maintenance and fault prediction of mechanical equipment.
Description
Technical Field
The invention belongs to the technical field of on-site detection of wear conditions of gears, and particularly relates to an in-situ three-dimensional reconstruction method for micro-topography of wear surfaces of gears.
Background
The gear is a common transmission part in mechanical equipment and is widely applied in the fields of engineering machinery, power generation equipment, transportation and the like. In the operation process of mechanical equipment, the surfaces of the friction pairs of the gears interact with each other, abrasion is inevitably generated, and the abrasion becomes a main reason of the failure of the gear transmission. According to different wear mechanisms, gear wear can be divided into adhesive wear, abrasive wear, fatigue wear and the like, and wear surfaces corresponding to different wear types also have different characteristics. Therefore, the appearance of the wear surface directly reflects the wear characteristics of the gear and is the most direct and main criterion for judging the wear mechanism. However, the traditional gear tooth surface wear state detection is generally used for fault analysis and tracing, the gear wear surface appearance is obtained by disassembling a gearbox and observing by naked eyes or slices, and the wear surface appearance detection of the gear in use is rare. The existing gear surface detection technology has two problems: 1) the detection result after disassembly can be used for fault analysis, but the fault development process cannot be reflected; 2) traditional visual inspection and two-dimensional surface inspection do not give quantitative volumetric wear information characteristics. Therefore, a three-dimensional shape acquisition method for detecting the gear wear state is developed, is used for accurately analyzing the process wear evolution of the gear friction pair, and has important significance for visual maintenance and fault prediction of mechanical equipment.
In the traditional manual detection, the wear condition of the surface of the gear is evaluated by depending on the experience by observing a two-dimensional image of the wear surface of the gear under a microscope by human eyes. Through the microscope, the inspector can only acquire the plane characteristics of the wear surface and cannot acquire the spatial characteristic information. Moreover, because the manual detection has subjectivity, the method has low detection efficiency and inaccurate detection result, and is easy to cause visual fatigue. Although a common gear measuring instrument, such as a three-coordinate measuring machine, can acquire surface three-dimensional information, the instrument needs to disassemble a gear and then place the gear in an experimental environment for measurement, field detection of the gear cannot be realized, and the instrument is expensive, complex in structure and high in requirement on comprehensive quality of a tester, so that application is restricted.
The advanced gear surface wear detection equipment is required to obtain accurate surface space data and color information while acquiring a micro three-dimensional morphology digital image of a wear surface on a gear working site so as to further perform wear fault analysis, wear mechanism identification and visual maintenance.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention aims to provide an in-situ three-dimensional reconstruction method for the microscopic morphology of the wear surface of the in-use gear, which is characterized in that the in-situ image acquisition system which is simple in operation and convenient to carry is built to obtain the wear surface images of the in-use gear under the irradiation of light sources at different angles; solving a gear wear surface normal vector by luminance information constraint of each point of the multiple images, and preliminarily recovering three-dimensional morphology information by the normal vector; then, microscopic three-dimensional reconstruction of the real surface of the gear is realized by surface height information polynomial fitting, surface color reduction and projection conversion; and finally, extracting a plurality of items of gear surface characteristic information from the height data so as to carry out further wear fault analysis, wear mechanism identification and visual maintenance.
In order to achieve the purpose, the invention adopts the following technical scheme:
the in-situ three-dimensional reconstruction method for the micro-topography of the worn surface of the gear comprises the following steps:
firstly, a portable in-situ image acquisition system is built, the portable in-situ image acquisition system comprises acquisition system hardware and acquisition system software, the acquisition system hardware comprises a miniature digital micro-camera 1, a controllable light source system 5 is arranged on the miniature digital micro-camera 1, the miniature digital micro-camera 1 is fixed on a universal bracket 2 through a high-precision slide rail 3 in the lens axis direction, and a magnetic adsorption type contact 4 for ensuring that a lens is vertical to a wear surface to be measured is arranged at the tail end of the miniature digital micro-camera 1; the reconstruction environment setting of the acquisition system software comprises the conversion between an image coordinate system and a camera coordinate system, wherein the camera coordinate system takes the optical center of the micro digital micro camera 1 as an original point, and the depth direction is a coordinate axis which is vertical to the surface to be measured;
establishing a near-field point light source illumination model, calibrating a light source space coordinate and illumination information, and calculating the position of a light source, the brightest light and the direction of a plane main optical axis based on a highlight sphere calibration method and a plane main optical axis calibration method;
thirdly, calculating a gear surface normal vector according to the calibrated light source direction and the acquired image information; obtaining preliminary depth information by a surface recovery algorithm, obtaining a microscopic reconstruction surface and height information thereof by polynomial fitting of the preliminary depth information, and recovering the real color of the surface by a color recovery method taking pixel points as units;
and fourthly, performing statistical calculation and section point calculation on the acquired height information to obtain characteristic parameter information on the surface of the gear.
The first step comprises the following steps:
step 1.1: the micro digital micro camera 1 is a collecting device, and the obtained gear surface area is 1mm2The working distance is 9mm, the bright part and the shadow change of the image sequence are obvious, and the requirements of the photometric stereo vision technology are met;
step 1.2: the controllable light source system 5 distributed annularly consists of eight annularly and uniformly distributed light sources and is controlled by a touch type change-over switch on the pen body of the miniature digital microscope camera 1;
step 1.3: the fixed support 2 is a universal support, so that the miniature digital micro-camera 1 can be ensured to be universally rotated to observe different-angle wear surfaces when being placed on the gear device, the high-precision slide rail 3 ensures that the miniature digital micro-camera 1 is finely adjusted by 0.1 mm in the direction of the lens axis, and the magnetic adsorption type contact 4 ensures that the lens axis is vertical to the surface to be detected, so that the reconstruction precision is ensured;
step 1.4: converting an image coordinate system and a camera coordinate system in acquisition system software, and establishing a matrix relation between an image pixel coordinate system and the camera coordinate system through a formula (1);
formula (1):
in the formula: u, v correspond to the column and row coordinates, X, of the image, respectivelyc、Yc、ZcRespectively corresponding to the coordinates of the camera in three directions in a Cartesian coordinate system; a isxIs an x-axis scale factor; a isyIs a scale factor on the y-axis; (u)0,v0) The coordinates of the intersection point of the optical axis of the camera and the image plane are obtained; and M is a camera internal parameter matrix.
The second step comprises the following steps:
step 2.1: the angle attenuation model of the near-field point light source accords with the g-cosine law, the distance attenuation model accords with the inverse square law, and the near-field point light source model with the illumination of a certain point R on the surface expressed by the formula (2) is obtained by combining the two illumination attenuation models:
formula (2):
in the formula E0G is an angle attenuation factor related to the light source light-emitting uniformity, and theta is an included angle between an incident light ray and the main optical axis;
step 2.2: calibrating the space coordinate of the light source when collecting the image, using the highlight sphere method, observing the incident angle equal to the highlight point when the lens is usedThe principle of the emergence angle is calibrated, and the relation expressed by the formula (3) and the normal direction of the known highlight point
Direction of viewing angle
To the direction of the light source
Solving is carried out;
formula (3):
step 2.3: the main light intensity of the brightest light and the main optical axis are calibrated, when a plane which is far away from a light source h is irradiated by a near-point light source, the total reflection brightness of all points R in the plane is expressed as a formula (4), a formula (5) can be obtained through formula derivation, and the main light intensity can be obtained through the formula (5); the main optical axis direction of the system is easy to determine due to the vertical downward property of the system light source;
formula (4):
formula (5):
wherein gamma is the included angle between the incident ray and the surface normal direction, and theta is the included angle between the incident ray and the main optical axis;
step 2.4: the attenuation factor is calibrated, and the angle attenuation factor g can be measured by the formula (6) through measuring the angle theta corresponding to the light intensity which is just half of the main light intensityhalfObtaining;
formula (6):
the third step comprises the following steps:
step 3.1: in-situ image sequence acquisition: sequentially opening single light sources at all angles, and shooting the surface image of the gear in situ;
3.2, filtering image noise by using a 3 × 3 Gaussian filter kernel to remove over-enhanced pixel points;
step 3.3, according to the internal parameters of the microscope and the light source space coordinates L (x) obtained in the steps (1) and (2)i,yi,zi) Main optical axis IiAnd main intensity of light Eio(ii) a Under 8 light sources, when a certain point R (x, y, z) on the gear surface is irradiated by the ith (i ═ 1, 2.., 8) light source, a corresponding incident light matrix exists
And a reflected luminance matrix
Using L ambert reflection model for point R, calculating normal vector n of corresponding pixel point by formula (7)PObtaining the normal vector of each pixel point in the image;
formula (7):
step 3.4: obtaining a preliminary reconstruction result, solving depth information of each pixel point in the image based on a Frankot-Chellappa (FC) algorithm, wherein the depth information is expressed as (u, v, delta w), calculating a z coordinate corresponding to each pixel point according to a formula (8) under the condition of a known focal length f, and calculating an x coordinate and a y coordinate of each pixel point according to a mapping relation of a formula (9), so that the obtaining of the preliminary reconstruction result is completed;
formula (8):
formula (9):
step 3.5: preliminary reconstruction information Z obtained from fourth-order polynomial pairs0Fitting to obtain a micro-reconstruction surfaceThe height data are stored in a matrix Z, and the fitting relation is expressed as a formula (10);
equation (10): gamma ═ p1x4+p2x3+p3x2+p4x+p5y4+p6y3+p7y2+p8y+p9
In the formula pi(i ═ 1, 2.., 9) as fitting parameters;
step 3.6: color restoration with pixel points as units; extracting reconstructed height data and writing the data into a matrix Z, and writing the RGB value of each pixel point into a matrix C; the two matrixes are used simultaneously, and the color of each pixel point is covered when each pixel point is reconstructed, so that the real color of the surface of the gear is restored;
step 3.7: converting the original parallel projection into perspective projection through projection conversion; the conversion relationship can be expressed as equation (11);
formula (11):
in the formula xc、yc、zcThe coordinate system respectively corresponds to the coordinate in three directions in a camera Cartesian coordinate system, and x, y and z respectively correspond to perspective projection coordinates.
The fourth step comprises the following steps:
step 4.1: and (4) statistically calculating the height information data of the microscopic surface in the height matrix Z stored in the step (3) to obtain the following three-dimensional characteristic parameters: surface arithmetic mean deviation SaRoot mean square deviation of surface SqSurface height distribution skewness SskKurtosis S of surface height distributionkuMaximum peak height SpMinimum valley depth SvThe sum of the maximum heights of the dimension-defining surfaces SzThe bearing area ratio S of the size-defining surfacemrVolume V of valley area of size-limiting surfacevvPeak bearing volume V of a size-defining surfacemp；
Step 4.2: statistically counting one row or one column in the height information data of the microscopic surface in the height matrix Z stored in the step 3And (4) calculating to obtain the following two-dimensional characteristic parameters: arithmetic mean deviation of contour RaAnd a height R of ten points of microscopic unevennesszMaximum height of profile Rq。
The invention is applied to the field of on-site detection of the worn surface of the gear, and has the following beneficial effects:
(1) the method is suitable for the field detection of the worn surface of the gear, and the acquisition of the microscopic three-dimensional morphology of the worn surface of the gear is quickly and efficiently realized.
(2) The invention builds an in-situ image acquisition system, has small volume, simple operation and convenient carrying, and can realize in-situ measurement and on-machine observation of the micro-topography of the surface of the gear.
(3) According to the method, the near-field point light source illumination model is established according to the actual light source position, so that the problem of larger curvature of the microcosmic reconstruction surface under the original parallel light model is greatly optimized.
(4) The method carries out surface fitting, color reduction and projection conversion on the preliminary reconstructed surface to obtain the gear micro-reconstruction surface with real color and real visual effect.
(5) The invention can extract the depth data of any point of the microcosmic reconstruction surface, thereby obtaining characteristic parameters with rich and comprehensive surface.
Drawings
FIG. 1 is a general flow diagram of in situ three-dimensional reconstruction of a gear wear surface microstructure.
Fig. 2 is a three-dimensional model diagram of the portable in-situ image capturing system, wherein fig. 2(a) is a front view and fig. 2(b) is a right view.
Fig. 3 is a sequence of images acquired by the portable in-situ image acquisition system on the gear surface 1.
Fig. 4(a) in fig. 4 is a normal vector diagram of the calculated micro-topography of the gear surface 1.
Fig. 4(b) in fig. 4 shows the preliminary reconstruction result of the gear surface 1.
Fig. 4(c) in fig. 4 is an in-situ three-dimensional reconstruction result of the micro-topography of the gear surface 1.
Fig. 5 is a sequence of images acquired by the portable in-situ image acquisition system on the gear surface 2.
Fig. 6(a) of fig. 6 is a normal vector diagram of the calculated micro-topography of the gear surface 2.
Fig. 6(b) in fig. 6 is a preliminary reconstruction result of the gear surface 2.
Fig. 6(c) in fig. 6 is the result of in-situ three-dimensional reconstruction of the micro-topography of the gear surface 2.
Detailed Description
The invention will be further illustrated with reference to the following figures and examples:
referring to fig. 1, an in-situ three-dimensional reconstruction method for a micro-topography of a worn surface of a gear comprises the following steps:
the method comprises the following steps: and (5) building a portable in-situ image acquisition system. The portable in-situ image acquisition system comprises acquisition system hardware and acquisition system software, and referring to fig. 2, the main body of the acquisition system hardware is a miniature digital micro camera 1, a controllable light source system 5 is arranged on the micro camera 1, the miniature digital micro camera 1 is fixed on a universal bracket 2 through a high-precision slide rail 3 in the axial direction of a lens, and a magnetic adsorption type contact 4 for ensuring that the lens is perpendicular to a wear surface to be measured is arranged at the tail end of the micro digital micro camera 1. The reconstruction environment setting of the acquisition system software comprises conversion between an image coordinate system and a camera coordinate system, wherein the camera coordinate system takes the optical center of the micro camera 1 as an original point, and the depth direction is a coordinate axis which is vertical to the surface to be measured.
The first step comprises the following steps:
step 1.1: the micro digital micro camera 1 is set as an image acquisition device of the system because of the characteristics of simple operation, convenient carrying and the like, and refers to and compares various three-dimensional surface acquisition instruments to acquire observation indexes, and the surface area of the acquired gear is about 1mm2. At the moment, the working distance is 9mm, the bright part and the shadow change of the image sequence are obvious, and the requirements of the photometric stereo technology are met.
Step 1.2: in order to obtain accurate surface three-dimensional information and provide reconstruction constraint conditions extracted in different angle directions, the controllable light source system 5 in annular distribution is composed of eight annularly and uniformly distributed light sources and is controlled by a touch type change-over switch on the pen body of the miniature digital microscope camera 1.
Step 1.3: the fixed support 2 is a universal support, can guarantee that the miniature digital micro-camera 1 can rotate universally to observe different-angle wear surfaces when being arranged on the gear device, the high-precision slide rail 3 guarantees that the miniature digital micro-camera 1 can be finely adjusted by 0.1 mm in the axial direction of the lens, and the magnetic adsorption type contact 4 guarantees that the axial direction of the lens is vertical to the surface to be measured, so that the reconstruction precision is guaranteed.
Step 1.4: the reconstruction method of the invention converts two-dimensional image information into three-dimensional space information, so that a corresponding image coordinate system and a camera coordinate system need to be established, and the relation between the two coordinate systems is established. Establishing a matrix relation between an image pixel coordinate system and a camera coordinate system through a formula (1);
formula (1):
in the formula: u, v correspond to the column and row coordinates, X, of the image, respectivelyc、Yc、ZcRespectively corresponding to the coordinates of three directions in a camera cartesian coordinate system. a isxIs an x-axis scale factor; a isyIs a scale factor on the y-axis; (u)0,v0) The coordinates of the intersection point of the optical axis of the camera and the image plane are obtained; and M is a camera internal parameter matrix.
Step two: establishing a near-field point light source illumination model, establishing the illumination model of the near-field point light source according to the actual light source condition of the system, calibrating the space coordinate and the illumination information of the light source, and calculating the position of the light source, the brightest light and the direction of a plane main optical axis based on a highlight sphere calibration method and a plane main optical axis calibration method.
The second step comprises the following steps:
step 2.1: the angle attenuation model of the near-field point light source accords with the g-cosine law, the distance attenuation model accords with the inverse square law, and the near-field point light source model with the illumination of a certain point R on the surface expressed by the formula (2) is obtained by combining the two illumination attenuation models:
formula (2):
in the formula E0G is an angle attenuation factor related to the light source light uniformity, and theta is the included angle between the incident light and the main optical axis.
Step 2.2: calibrating the space coordinate of the light source when collecting the image, using the highlight sphere method, calibrating by using the principle that the incident angle is equal to the emergent angle at the highlight point when the lens observes the highlight, and the relation expressed by the formula (3) and the known normal direction of the highlight point
Direction of viewing angle
To the direction of the light source
Solving is carried out;
formula (3):
step 2.3: the main light intensity and the main optical axis of the brightest light are calibrated, when a plane which is far away from a light source h is irradiated by a near-point light source, the total reflection brightness of all points R in the plane can be expressed as a formula (4), a formula (5) can be obtained through formula derivation, the main light intensity can be obtained through the formula (5), and the main optical axis direction of the system is easy to determine due to the vertical downward property of the light source of the system;
formula (4):
formula (5):
wherein gamma is the included angle between the incident ray and the surface normal direction, and theta is the included angle between the incident ray and the main optical axis;
step 2.4: the attenuation factor is calibrated, and the angle attenuation factor g can be measured by the formula (6) through measuring the angle theta corresponding to the light intensity which is just half of the main light intensityhalfObtaining;
formula (6):
step three: calculating a gear surface normal vector according to the calibrated light source direction and the acquired image information; obtaining preliminary depth information by a surface recovery algorithm, obtaining a microscopic reconstruction surface by polynomial fitting of the preliminary depth information, and recovering the real color of the surface by a color recovery method taking pixel points as units;
the third step comprises the following steps:
step 3.1: acquiring an image sequence in situ, sequentially opening single light sources at various angles, and shooting a gear surface image in situ; fig. 3 is a sequence of images acquired by the image acquisition system on the gear surface 1, and fig. 5 is a sequence of images acquired by the image acquisition system on the gear surface 2;
3.2, filtering image noise by using a 3 × 3 Gaussian filter kernel to remove over-enhanced pixel points;
step 3.3, obtaining the internal parameters of the microscope and the light source space coordinates L (x) according to the step 1 and the step 2i,yi,zi) Main optical axis IiAnd main intensity of light Eio(ii) a Under 8 light sources, when a certain point R (x, y, z) on the gear surface is irradiated by the ith (i ═ 1, 2.., 8) light source, a corresponding incident light matrix exists
And a reflected luminance matrix
Using L ambert reflection model for point R, calculating normal vector n of corresponding pixel point by formula (7)P(ii) a Thus, the normal vector of each pixel point in the image is obtained; FIG. 4(a) is a normal vector diagram of the calculated micro-topography of the gear surface 1, and FIG. 6(a) is a normal vector diagram of the calculated micro-topography of the gear surface 2;
formula (7):
step 3.4: obtaining a preliminary reconstruction result, and solving the depth information of each pixel point in the image based on a Frankot-Chellappa (FC) algorithm, wherein the depth information is expressed as (u, v, delta w); under the condition of known focal length f, calculating a z coordinate corresponding to each pixel point according to a formula (8); calculating the x and y coordinates of each pixel point according to the mapping relation of the formula (9); thus, the acquisition of the primary reconstruction result is completed; fig. 4(b) is a result of preliminary reconstruction of the gear surface 1, and fig. 6(b) is a result of preliminary reconstruction of the gear surface 2;
formula (8):
formula (9):
step 3.5: preliminary reconstruction information Z obtained from fourth-order polynomial pairs0Fitting to obtain a microscopic reconstruction surface, storing the height data to a matrix Z, and expressing the fitting relation as a formula (10);
equation (10): gamma ═ p1x4+p2x3+p3x2+p4x+p5y4+p6y3+p7y2+p8y+p9
In the formula pi(i ═ 1, 2.., 9) as fitting parameters;
step 3.6: and (4) color restoration with pixel points as units, extracting reconstructed height data and writing the data into a matrix Z, and writing the RGB value of each pixel point into a matrix C. The two matrixes are used simultaneously, and the color of each pixel point is covered when each pixel point is reconstructed, so that the real color of the surface of the gear is restored;
step 3.7: converting the original parallel projection into perspective projection through projection conversion, wherein the conversion relation can be expressed as a formula (11); obtaining a real microscopic reconstruction surface through color reduction and perspective projection; FIG. 4(c) is an in-situ three-dimensional reconstruction result of the micro-topography of the gear surface 1, and FIG. 6(c) is an in-situ three-dimensional reconstruction result of the micro-topography of the gear surface 2;
formula (11):
in the formula xc、yc、zcRespectively corresponding to coordinates in three directions in a camera Cartesian coordinate system, and respectively corresponding to perspective projection coordinates in x, y and z;
step four: performing statistical calculation and section point calculation on the acquired height information to obtain characteristic parameter information on the surface of the gear;
the fourth step comprises the following steps:
step 4.1: and (4) statistically calculating the height information data of the microscopic surface in the height matrix Z stored in the step (3) to obtain the following three-dimensional characteristic parameters: surface arithmetic mean deviation SaRoot mean square deviation of surface SqSurface height distribution skewness SskKurtosis S of surface height distributionkuMaximum peak height SpMinimum valley depth SvThe sum of the maximum heights of the dimension-defining surfaces SzThe bearing area ratio S of the size-defining surfacemrVolume V of valley area of size-limiting surfacevvPeak bearing volume V of a size-defining surfacemp；
Step 4.2: and (3) performing statistical calculation on one row or one column in the height information data of the microscopic surface in the height matrix Z stored in the step (3) to obtain the following two-dimensional characteristic parameters: arithmetic mean deviation of contour RaAnd a height R of ten points of microscopic unevennesszMaximum height of profile Rq。
Claims (5)
1. The in-situ three-dimensional reconstruction method for the micro-topography of the worn surface of the gear is characterized by comprising the following steps of:
firstly, a portable in-situ image acquisition system is built, the portable in-situ image acquisition system comprises acquisition system hardware and acquisition system software, the acquisition system hardware comprises a miniature digital micro-camera (1), a controllable light source system (5) is arranged on the miniature digital micro-camera (1), the miniature digital micro-camera (1) is fixed on a universal support (2) through a high-precision slide rail (3) in the lens axis direction, and a magnetic adsorption type contact (4) for ensuring that a lens is vertical to a to-be-detected wear surface is arranged at the tail end of the miniature digital micro-camera (1); the reconstruction environment setting of the acquisition system software comprises the conversion between an image coordinate system and a camera coordinate system, wherein the camera coordinate system takes the optical center of the miniature digital micro camera (1) as an original point, and the depth direction is taken as a coordinate axis and is vertical to the surface to be measured;
establishing a near-field point light source illumination model, calibrating a light source space coordinate and illumination information, and calculating the position of a light source, the brightest light and the direction of a plane main optical axis based on a highlight sphere calibration method and a plane main optical axis calibration method;
thirdly, calculating a gear surface normal vector according to the calibrated light source direction and the acquired image information; obtaining preliminary depth information by a surface recovery algorithm, obtaining a microscopic reconstruction surface and height information thereof by polynomial fitting of the preliminary depth information, and recovering the real color of the surface by a color recovery method taking pixel points as units;
and fourthly, performing statistical calculation and section point calculation on the acquired height information to obtain characteristic parameter information on the surface of the gear.
2. The in-situ three-dimensional reconstruction method of the micro-topography of the wear surface of the gear according to claim 1, wherein the first step comprises the steps of:
step 1.1: the micro digital micro camera (1) is a collecting device, and the obtained gear surface area is 1mm2The working distance is 9mm, the bright part and the shadow change of the image sequence are obvious, and the requirements of the photometric stereo vision technology are met;
step 1.2: the controllable light source system (5) which is distributed annularly consists of eight light sources which are uniformly distributed annularly and is controlled by a touch change-over switch on the pen body of the miniature digital microscope camera (1);
step 1.3: the fixed support (2) is a universal support, so that the miniature digital micro-camera (1) can be ensured to be universally rotated to observe abrasion surfaces with different angles when being placed on a gear device, the high-precision slide rail (3) ensures that the miniature digital micro-camera (1) is finely adjusted by 0.1 mm in the direction of the axis of the lens, and the magnetic adsorption type contact (4) ensures that the axis of the lens is vertical to the surface to be measured, so that the reconstruction precision is ensured;
step 1.4: converting an image coordinate system and a camera coordinate system in acquisition system software, and establishing a matrix relation between an image pixel coordinate system and the camera coordinate system through a formula (1);
formula (1):
in the formula: u, v correspond to the column and row coordinates, X, of the image, respectivelyc、Yc、ZcRespectively corresponding to the coordinates of the camera in three directions in a Cartesian coordinate system; a isxIs an x-axis scale factor; a isyIs a scale factor on the y-axis; (u)0,v0) The coordinates of the intersection point of the optical axis of the camera and the image plane are obtained; and M is a camera internal parameter matrix.
3. The in-situ three-dimensional reconstruction method of the micro-topography of the wear surface of the gear according to claim 1, wherein the second step comprises the steps of:
step 2.1: the angle attenuation model of the near-field point light source accords with the g-cosine law, the distance attenuation model accords with the inverse square law, and the near-field point light source model with the illumination of a certain point R on the surface expressed by the formula (2) is obtained by combining the two illumination attenuation models:
formula (2):
in the formula E0G is an angle attenuation factor related to the light source light-emitting uniformity, and theta is an included angle between an incident light ray and the main optical axis;
step 2.2: calibrating the spatial coordinates of the light source during image acquisition using a highlight sphere methodThe principle that the incident angle is equal to the emergent angle at the highlight point when the lens observes the highlight is utilized for calibration, and the relation expressed by the formula (3) and the known normal direction at the highlight point are used for calibration
Direction of viewing angle
To the direction of the light source
Solving is carried out;
formula (3):
step 2.3: the main light intensity of the brightest light and the main optical axis are calibrated, when a plane which is far away from a light source h is irradiated by a near-point light source, the total reflection brightness of all points R in the plane is expressed as a formula (4), a formula (5) can be obtained through formula derivation, and the main light intensity can be obtained through the formula (5); the main optical axis direction of the system is easy to determine due to the vertical downward property of the system light source;
formula (4):
formula (5):
wherein gamma is the included angle between the incident ray and the surface normal direction, and theta is the included angle between the incident ray and the main optical axis;
step 2.4: calibrating an attenuation factor; the angle attenuation factor g can be obtained by the formula (6) by measuring the angle theta corresponding to the light intensity being just half of the main light intensityhalfObtaining;
formula (6):
4. the in-situ three-dimensional reconstruction method of the micro-topography of the wear surface of the gear according to claim 1, wherein the third step comprises the steps of:
step 3.1: in-situ image sequence acquisition: sequentially opening single light sources at all angles, and shooting the surface image of the gear in situ;
3.2, filtering image noise by using a 3 × 3 Gaussian filter kernel to remove over-enhanced pixel points;
step 3.3, according to the internal parameters of the microscope and the light source space coordinates L (x) obtained in the step one and the step twoi,yi,zi) Main optical axis IiAnd main intensity of light Eio(ii) a Under 8 light sources, a certain point R (x, y, z) on the surface of the gear has a corresponding incident light matrix when being irradiated by the ith light source
And a reflected luminance matrix
1,2,3 …,8, calculating normal vector n of corresponding pixel point by using L ambert reflection model for point R and using formula (7)PObtaining a normal vector of each pixel point in the image;
formula (7):
step 3.4: obtaining a preliminary reconstruction result, solving depth information of each pixel point in the image based on a Frankot-Chellappa (FC) algorithm, wherein the depth information is expressed as (u, v, delta w), under the condition of known focal length f, calculating a z coordinate corresponding to each pixel point according to a formula (8), and calculating an x coordinate and a y coordinate of each pixel point according to a mapping relation of a formula (9), so that the preliminary reconstruction result is obtained;
formula (8):
formula (9):
step 3.5: preliminary reconstruction information Z obtained from fourth-order polynomial pairs0Fitting to obtain a microscopic reconstruction surface, storing the height data to a matrix Z, and expressing the fitting relation as a formula (10);
equation (10): gamma ═ p1x4+p2x3+p3x2+p4x+p5y4+p6y3+p7y2+p8y+p9
In the formula pi(i ═ 1, 2.., 9) as fitting parameters;
step 3.6: color restoration with pixel points as units; extracting reconstructed height data and writing the data into a matrix Z, and writing the RGB value of each pixel point into a matrix C; the two matrixes are used simultaneously, and the color of each pixel point is covered when each pixel point is reconstructed, so that the real color of the surface of the gear is restored;
step 3.7: converting the original parallel projection into perspective projection through projection conversion; the conversion relationship can be expressed as equation (11);
formula (11):
in the formula xc、yc、zcThe coordinate system respectively corresponds to the coordinate in three directions in a camera Cartesian coordinate system, and x, y and z respectively correspond to perspective projection coordinates.
5. The in-situ three-dimensional reconstruction method of the micro-topography of the wear surface of the gear according to claim 1, wherein the fourth step comprises the steps of:
step 4.1: and (4) statistically calculating the height information data of the microscopic surface in the height matrix Z stored in the step (3) to obtain the following three-dimensional characteristic parameters: surface arithmetic mean deviation SaRoot mean square deviation of surface SqHigh surface areaSkewness S of degree distributionskKurtosis S of surface height distributionkuMaximum peak height SpMinimum valley depth SvThe sum of the maximum heights of the dimension-defining surfaces SzThe bearing area ratio S of the size-defining surfacemrVolume V of valley area of size-limiting surfacevvPeak bearing volume V of a size-defining surfacemp；
Step 4.2: and (3) performing statistical calculation on one row or one column in the height information data of the microscopic surface in the height matrix Z stored in the step (3) to obtain the following two-dimensional characteristic parameters: arithmetic mean deviation of contour RaAnd a height R of ten points of microscopic unevennesszMaximum height of profile Rq。
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