阅读说明：本技术 一种高温表面线激光几何测量误差分析方法 (High-temperature surface line laser geometric measurement error analysis method ) 是由 王永青 苗子健 薄其乐 刘海波 刘晓宇 邢祥胜 李特 于 2021-08-06 设计创作，主要内容包括：本发明属于几何量测试技术领域,提供了一种高温表面线激光几何测量误差分析方法。该方法首先对高温工件附近空气温度场进行模拟计算,得到空气的温度分布状态后,计算空间内各点折射率大小；结合折射定律计算得到不同空间位置处的激光折射角；基于反向光线追迹方法得到高温表面对应的成像点,根据激光三角法计算该成像点对应测量距离,对比实际距离和理想距离得到高温条件下的测量误差。对高温构件附近空气温度场进行分析,将传热简化为一维热传导问题,计算得到空气温度分布状态,有效简化了计算过程。结合高温条件下的温度-折射率关联公式得到不同对应的空气折射率大小,与常温条件下的关联公式相比有效提高了折射率计算精度。(The invention belongs to the technical field of geometric measurement and provides a method for analyzing geometric measurement errors of high-temperature surface line laser. Firstly, performing analog calculation on an air temperature field near a high-temperature workpiece to obtain the temperature distribution state of air, and then calculating the refractive index of each point in space; calculating to obtain laser refraction angles at different spatial positions by combining refraction laws; and obtaining an imaging point corresponding to the high-temperature surface based on a reverse ray tracing method, calculating a corresponding measurement distance of the imaging point according to a laser triangulation method, and comparing the actual distance with the ideal distance to obtain a measurement error under the high-temperature condition. The air temperature field near the high-temperature component is analyzed, heat transfer is simplified into a one-dimensional heat conduction problem, the air temperature distribution state is obtained through calculation, and the calculation process is effectively simplified. Different corresponding air refractive index values are obtained by combining a temperature-refractive index correlation formula under a high temperature condition, and the refractive index calculation precision is effectively improved compared with the correlation formula under a normal temperature condition.)

1. A high-temperature surface line laser geometric measurement error analysis method comprises the steps of firstly, carrying out simulation calculation on an air temperature field near a high-temperature workpiece to obtain the temperature distribution state of air, and then calculating the refractive index of each point in space; calculating to obtain laser refraction angles at different spatial positions by combining refraction laws; obtaining an imaging point corresponding to the high-temperature surface based on a reverse ray tracing method, calculating a corresponding measurement distance of the imaging point according to a laser triangulation method, and comparing an actual distance with an ideal distance to obtain a measurement error under a high-temperature condition;

the method is characterized by comprising the following steps:

(1) high temperature surface air temperature field calculation

The direct heat exchange between the high-temperature component and the air is approximately one-dimensional heat conduction, and the temperature of the air at the position d away from the high-temperature surface is considered as room temperature; the one-dimensional steady-state thermal conductivity differential equation is expressed as:

wherein T is the air temperature, and z is the spatial position coordinate; heat conductivity coefficient lambda of air_airTo reduce to a constant, equation (1) reduces to:

taking the boundary point of the heat affected zone as an origin, the boundary conditions of the equation are as follows:

wherein, T₁At room temperature, T₂Is the temperature of the surface of the high temperature component; the following is obtained according to formula (2) and formula (3):

integrating the above equation to obtain an expression of the air temperature distribution from the thermal boundary to the surface of the high-temperature member:

(2) air refractive index calculation

According to the step (1), calculating the refractive index of air at different positions by combining an empirical formula of temperature and refractive index; the refractive index of air at elevated temperatures is calculated using the extended Raeger empirical formula:

wherein n is the refractive index of air, a_i(i ═ 0,1,2,3,4) for the spreading factor, P for the air pressure, and λ for the laser wavelength;

(3) imaging point position calculation

Establishing a space coordinate system XOZ, wherein an origin O is positioned at the measuring range midpoint in the height direction of the sensor, an OX axis is vertical to a laser plane and takes the direction close to the photosensitive array as positive, an OZ axis is vertical to the surface of a workpiece and takes the direction close to the sensor as positive, and the central coordinate of a receiving lens of the sensor is recorded as (x)₀,z₀) And the sensor photosensitive array coordinate is marked as (x)_c,z_c) And the coordinate of the central point of the photosensitive array is (x)_c0,z_c0) (ii) a When the high temperature plane is located at z ═ z_hWhen the thermal boundary is located at z ═ z_h+ d; according to the ray reverse tracing algorithm, the photosensitive point (x) on the photosensitive array_ci,z_ci) The corresponding coordinate when the corresponding ray reaches the thermal boundary is noted as (x)_hbi,z_hbi) And calculating according to the geometric relationship to obtain:

with a point (x)_hbi,z_hbi) Establishing a spatial coordinate system X as the origin of coordinates_LO_LZ_L；O_LX_LAxis perpendicular to the laser plane, O_LZ_LThe axis is vertical to the surface of the workpiece and takes the direction close to the surface to be measured as positive; the light ray track can deflect after entering a heat affected zone, and the laser refraction angle of each point in the propagation process is calculated according to the refraction law:

wherein n (z)_l) Is a distance z from the thermal boundary_lRefractive index of air, theta (z)_l) Is a distance z from the thermal boundary_lAngle of refraction of the laser, n₀Is the corresponding air index at the thermal boundary; theta₀The corresponding laser refraction angle of the light at the thermal boundary is obtained by calculation:

in the reverse ray tracing process, the ray motion trail satisfies the equation:

dx_l＝tanθ(z_l)dz_l(10)

integrating the above formula to obtain the corresponding transverse offset x at the position where the distance h from the optical path to the thermal boundary is_l：

When the ray path intersects the laser plane, i.e. x_l＝x_hbiThe time reverse ray tracing stops, and the corresponding height coordinate is recorded as z_li(ii) a The judgment criterion for determining the imaging point according to the imaging principle is as follows:

when z is_liWhen d, point (x)_hbi,z_li) The point where the laser plane intersects with the surface to be measured corresponds to a photosite (x)_ci,z_ci) Imaging points of the surface to be measured;

(z is when z)_liNot equal to d, point (x)_hbi,z_li) Is not the intersection point of the laser plane and the surface to be measured, and has no light sensitive point (x) corresponding to the light ray_ci,z_ci) Receiving, namely the photosite is not an imaging point;

(4) line laser measurement error calculation

Through traversing all the photosensitive points, obtaining the corresponding actual imaging point (x) of the high-temperature surface_c,z_c) (ii) a Calculating the corresponding measuring distance of an actual imaging point in an ideal environment according to a laser triangulation method:

wherein alpha is an included angle between a connecting line of the measuring point and the optical center of the receiving lens group and the laser plane; gamma is the image point and the optical center line of the receiving lens group and the plane of the photosensitive arrayAn included angle; l is the distance from the optical center of the receiving lens group to the measuring point; l' is the distance from the optical center of the receiving lens group to an imaging point on the photosensitive array; delta is the imaging point (x)_c,z_c) The corresponding image displacement on the photosensitive plane is calculated by the following formula:

the measurement error due to the high temperature condition is calculated as:

error＝z_h-Δ (14)。

Technical Field

The invention belongs to the technical field of geometric measurement, and particularly relates to a high-temperature surface line laser geometric measurement error analysis method.

Background

The on-machine measurement of the geometric dimension under the high-temperature severe working condition relates to the fields of aerospace, automobile manufacturing, welding forging and other mechanical industries. Taking a rocket fuel storage tank as an example, the rocket fuel storage tank is formed by oppositely assembling and welding a plurality of sections of cylinders; the position of the butt joint surface deviates from the theoretical position due to the influence of factors such as extrusion and the like in the welding process, and welding defects can be generated if the position and the posture of the stirring head are not adjusted according to the actual position of the butt joint surface; therefore, the step difference, the gap and other local geometric characteristics of the butt joint surface of the cylinder body need to be detected in real time in the welding process. Local high temperature is generated on the surface in the welding process (the temperature of a welding center is as high as nearly 600 ℃), and if the traditional contact type measuring sensor is used for prepositive measurement, the sensor can be failed or even damaged due to high-temperature heat conduction, and on-machine high-precision detection cannot be carried out. The line laser scanning technology has the advantages of simple structure, mature technology, high scanning precision and the like, and is more and more widely used in the field of measurement and processing integration. However, a heat exchange process exists between the high-temperature surface and the air, so that the temperature of the air medium is not uniform, the air temperature can be changed along with the time, the refractive index is changed in a nonlinear mode in the laser transmission process, and the measurement result is difficult to accurately reflect the geometric information of the high-temperature surface.

In 2015, CN201510100946.X discloses an image quality compensation method in high-temperature object measurement, and aiming at the problem of high-temperature object radiation highlight, a dimmable highlight laser is adopted to irradiate a high-temperature surface, the light intensity of the laser is adjusted in real time according to the light intensity variation trend of the amplitude light in the pass band of the optical filter at different temperatures, and the clear imaging of the characteristic light strip of the high-temperature object with large temperature gradient is realized. In a paper, namely a laser scanning-based annular forging radial dimension measurement method, by Li swarm et al, for the problem of excessive data noise when a high-temperature forging is measured by laser scanning, preprocessing of measurement point cloud based on an information space set and a consistency continuity coefficient is provided, and measurement data with high precision is obtained. The method improves the measurement accuracy of the system from the angles of an imaging process and point cloud pretreatment, and measurement errors caused by the refraction of laser in a medium with variable temperature are not mentioned.

Disclosure of Invention

The invention mainly solves the technical problem of overcoming the defects of the method and invents a method for analyzing geometric measurement errors of high-temperature surface line laser aiming at the problem of nonlinear transmission of variable-temperature medium laser. Analyzing an air temperature field near a high-temperature surface, and determining the refractive index distribution state of each position between the high-temperature surface and a linear laser sensor by combining an empirical formula of temperature and refractive index; calculating to obtain laser refraction angles at different spatial positions according to a refraction angle calculation formula; aiming at the problem of laser nonlinear propagation, solving the actual propagation path and the actual imaging point position of the laser by adopting a reverse ray tracing algorithm; and calculating a corresponding distance value of an imaging point under a normal temperature condition according to a laser triangulation method, and comparing the distance value with an actual distance to obtain a line laser measurement error caused by a high-temperature surface.

The technical scheme of the invention is as follows:

a high-temperature surface line laser geometric measurement error analysis method comprises the steps of firstly, carrying out simulation calculation on an air temperature field near a high-temperature workpiece to obtain the temperature distribution state of air, and then calculating the refractive index of each point in space; calculating to obtain laser refraction angles at different spatial positions by combining refraction laws; obtaining an imaging point corresponding to the high-temperature surface based on a reverse ray tracing method, calculating a corresponding measurement distance of the imaging point according to a laser triangulation method, and comparing an actual distance with an ideal distance to obtain a measurement error under a high-temperature condition;

the method comprises the following specific steps:

(1) high temperature surface air temperature field calculation

The direct heat exchange between the high-temperature component and the air is approximately one-dimensional heat conduction, and the temperature of the air at the position d away from the high-temperature surface is considered as room temperature; the one-dimensional steady-state thermal conductivity differential equation is expressed as:

wherein T is the air temperature, and z is the spatial position coordinate; heat conductivity coefficient lambda of air_airTo reduce to a constant, equation (1) reduces to:

taking the boundary point of the heat affected zone as an origin, the boundary conditions of the equation are as follows:

wherein, T₁At room temperature, T₂Is the temperature of the surface of the high temperature component; the following is obtained according to formula (2) and formula (3):

integrating the above equation to obtain an expression of the air temperature distribution from the thermal boundary to the surface of the high-temperature member:

(2) air refractive index calculation

According to the step (1), calculating the refractive index of air at different positions by combining an empirical formula of temperature and refractive index; the refractive index of air at elevated temperatures is calculated using the extended Raeger empirical formula:

wherein n is the refractive index of air, a_i(i ═ 0,1,2,3,4) for the spreading factor, P for the air pressure, and λ for the laser wavelength;

(3) imaging point position calculation

Establishing a space coordinate system XOZ, wherein an origin O is positioned at the measuring range midpoint in the height direction of the sensor, an OX axis is vertical to a laser plane and takes the direction close to the photosensitive array as positive, an OZ axis is vertical to the surface of a workpiece and takes the direction close to the sensor as positive, and the central coordinate of a receiving lens of the sensor is recorded as (x)₀,z₀) And the sensor photosensitive array coordinate is marked as (x)_c,z_c) And the coordinate of the central point of the photosensitive array is (x)_c0,z_c0) (ii) a When the high temperature plane is located at z ═ z_hWhen the thermal boundary is located at z ═ z_h+ d; according to the ray reverse tracing algorithm, the photosensitive point (x) on the photosensitive array_ci,z_ci) The corresponding coordinate when the corresponding ray reaches the thermal boundary is noted as (x)_hbi,z_hbi) And calculating according to the geometric relationship to obtain:

with a point (x)_hbi,z_hbi) Establishing a spatial coordinate system X as the origin of coordinates_LO_LZ_L；O_LX_LAxis perpendicular to the laser plane, O_LZ_LThe axis is vertical to the surface of the workpiece and takes the direction close to the surface to be measured as positive; the light ray track can deflect after entering a heat affected zone, and the laser refraction angle of each point in the propagation process is calculated according to the refraction law:

wherein n (z)_l) Is a distance z from the thermal boundary_lRefractive index of air, theta (z)_l) Is a distance z from the thermal boundary_lAngle of refraction of the laser, n₀Is the corresponding air index at the thermal boundary; theta₀The corresponding laser refraction angle of the light at the thermal boundary is obtained by calculation:

in the reverse ray tracing process, the ray motion trail satisfies the equation:

dx_l＝tanθ(z_l)dz_l (10)

integrating the above formula to obtain the corresponding transverse offset x at the position where the distance h from the optical path to the thermal boundary is_l：

When the ray path intersects the laser plane, i.e. x_l＝x_hbiThe time reverse ray tracing stops, and the corresponding height coordinate is recorded as z_li(ii) a The judgment criterion for determining the imaging point according to the imaging principle is as follows:

when z is_liWhen d, point (x)_hbi,z_li) The point where the laser plane intersects with the surface to be measured corresponds to a photosite (x)_ci,z_ci) Imaging points of the surface to be measured;

(z is when z)_liNot equal to d, point (x)_hbi,z_li) Is not the intersection point of the laser plane and the surface to be measured, and has no light sensitive point (x) corresponding to the light ray_ci,z_ci) Receiving, namely the photosite is not an imaging point;

(4) line laser measurement error calculation

Through traversing all the photosensitive points, obtaining the corresponding actual imaging point (x) of the high-temperature surface_c,z_c) (ii) a Calculating the corresponding measuring distance of an actual imaging point in an ideal environment according to a laser triangulation method:

wherein alpha is an included angle between a connecting line of the measuring point and the optical center of the receiving lens group and the laser plane; gamma is an included angle between a connecting line of the imaging point and the optical center of the receiving lens group and the plane of the photosensitive array; l is the distance from the optical center of the receiving lens group to the measuring point; l' is the light of the receiving lens groupThe distance from the optical center to an imaging point on the photosensitive array; delta is the imaging point (x)_c,z_c) The corresponding image displacement on the photosensitive plane is calculated by the following formula:

the measurement error due to the high temperature condition is calculated as:

error＝z_h-Δ (14)。

the invention has the beneficial effects that:

1. the air temperature field near the high-temperature component is analyzed, heat transfer is simplified into a one-dimensional heat conduction problem, the air temperature distribution state is obtained through calculation, and the calculation process is effectively simplified.

2. Different corresponding air refractive index values are obtained by combining a temperature-refractive index correlation formula under a high temperature condition, and the refractive index calculation precision is effectively improved compared with the correlation formula under a normal temperature condition.

3. According to the reverse ray tracing theory and the refraction law, the actual imaging point corresponding to the high-temperature surface is solved, the high-temperature surface laser measurement error is obtained by comparing the measurement distance corresponding to the imaging point in the ideal environment, and the high-temperature surface line laser geometric measurement accuracy can be effectively improved.

Drawings

FIG. 1 is a flow chart of high temperature surface line laser measurement error compensation;

FIG. 2 is a schematic view of high temperature components and air heat conduction;

FIG. 3 is a schematic diagram of a reverse ray trace;

FIG. 4 is a schematic illustration of laser measurement error;

fig. 5 is an error generated by measuring surfaces at different distances at different temperatures.

In the figure: 1-high temperature surface, 2-air, 3-thermal boundary.

Detailed Description

The following describes embodiments of the present invention in detail with reference to the accompanying drawings and technical solutions.

(1) High temperature surface air temperature field calculation

The heat exchange between the high-temperature surface and the air is approximate to the one-dimensional heat conduction problem, the air at the position with the distance of 30mm from the high-temperature surface reaches the room temperature, meanwhile, the heat conductivity coefficient of the air is set to be constant, the boundary point of the heat affected zone is used as the origin, and the boundary conditions of the equation are set as follows: z-0 (i.e. thermal boundary) temperature T₁At 27 deg.C, z is the temperature T at 30mm (i.e. the workpiece surface)₂100 ℃, 200 ℃, 300 ℃, 400 ℃. An expression of the air temperature from the thermal boundary to the surface of the high-temperature component under different temperature conditions can be obtained according to the heat conduction differential equation.

(2) Air refractive index distribution calculation

Calculating the refractive index of the air at different positions by combining the refractive index of the air under a high temperature condition and adopting an expanded Raeger empirical formula according to the temperature expression obtained by calculation in the step (1); wherein the expansion coefficient a₀＝-0.0002，a₁＝1.453，a₂＝-121.495，a₃＝-1.004，a₄-0.005, 101325Pa for air pressure and 405nm for laser wavelength. The magnitude of the refractive index can be expressed as:

(3) imaging point position calculation

Assuming that the position coordinate of the high-temperature plane in the measuring range of the on-line laser sensor is z ═ z, the position coordinate of the high-temperature plane in the space coordinate system XOZ is set as_h,z_hE (-2.4,2.4), and the thermal boundary position is z ═ z_h+30,z_hEpsilon (-2.4, 2.4); and (3) setting coordinates of each point by utilizing a line laser sensor structure: receive lens center coordinates (39.72,52.71), photosensitive array center point coordinates (75.8287,100.6281); obtaining photosites (x) according to the geometrical relation_ci,z_ci) And its corresponding thermal boundary point (x)_hbi,z_hbi) And simultaneously calculating the refraction angle n of the light at the thermal boundary₀Calculating the refraction angles of the light rays at different positions by combining the law of refraction so as to obtain a light ray track equation through integration, solving the light ray tracing end point coordinate corresponding to the light sensing point, and calculating the light ray tracing end point coordinate according to the light ray tracing end point coordinateTraversing all photosites to find the position z_hAt the imaging point (x) corresponding to the high temperature plane_c,z_c)。

(4) Line laser measurement error calculation

Setting the structural parameters of the line laser sensor: α is 37 °, γ is 70 °, l is 66mm, l' is 60 mm; firstly, fixing the temperature of the surface to be measured unchanged, calculating the image displacement z 'corresponding to an imaging point, substituting the image displacement z' into a laser triangulation formula to calculate the measurement distance corresponding to the imaging point under an ideal condition, and comparing the measurement distance with the position of a high-temperature plane to obtain a measurement error; the surface temperature of the workpiece is changed to be repeatedly calculated, so that the measurement errors of the linear laser sensor corresponding to different temperatures and different measurement distances are obtained, and the calculation result is shown in fig. 5.

The method for compensating the geometric measurement error of the laser on the high-temperature surface line can compensate the error by calculating the refraction deviation of a light path when the laser is transmitted in the air with variable temperature, has strong measurement adaptability, and can meet the requirement of high-precision measurement of the geometric measurement of the high-temperature surface.