A method for measuring field deformation analysis under non-uniform temperature fields of large tooling

Abstract

The present invention discloses a method for measuring field deformation analysis under non-uniform temperature fields of large toolings, which comprises the following steps: constructing a finite element model of an aircraft tooling; designing a measurement scheme; performing finite element simulation calculations; and calibrating a simulation model. The present invention can perform deformation calculations for large toolings under non-uniform temperature fields. The correlation analysis between the actual measurement results and the calculation results proves that the calculation method has high precision. Compared with the measurement errors caused by temperature in traditional large tooling measurements where the influence of temperature is not considered, the present invention can calculate the thermal deformation of toolings under non-uniform temperatures, compensate for the influence of temperature on the measurement field, and further improve the measurement precision of the deformation of large toolings.

Description

Technical Field

[0001] The present invention relates to a prediction technology for the deformation of a large fixture under a non-uniform temperature field, specifically a method for obtaining the thermal deformation simulation results of a large fixture under a non-uniform temperature field. Background Art

[0002] In aircraft digital assembly measurement, the accuracy of a laser tracker determines the measurement accuracy and assembly quality. At the assembly site of a large fixture, due to the complex on-site environment, large structural span of the fixture, high degree of static indeterminacy, and large local extreme temperature difference of the fixture, the large fixture is in a non-uniform temperature field as a whole. The non-uniform temperature field will cause thermal deformation and thermal stress inside the fixture. The common observation points arranged on the fixture will have different degrees of thermal deformation with temperature changes, resulting in the coordinates of the observation points deviating from the theoretical positions. The non-uniform temperature field in the actual measurement process will cause the measurement field accuracy formed by the fitting of the measured data and the theoretical data of the common observation points to decrease, unable to meet the assembly measurement requirements. Therefore, aiming at the problem of excessive thermal deformation error caused by the non-uniform temperature field, a method for analyzing the deformation of the measurement field of a large fixture under a non-uniform temperature field needs to be proposed. Summary of the Invention

[0003] The present invention can perform thermal deformation simulation calculations on a large fixture under a non-uniform temperature field. Through the correlation analysis of the actual measurement results and the calculation results, it is proved that the calculation method has high accuracy. Compared with the measurement error caused by temperature in the traditional measurement of large fixtures without considering the temperature effect, the present invention can calculate the thermal deformation of the fixture under non-uniform temperature, compensate for the influence of temperature on the measurement field, and further improve the measurement accuracy of the fixture deformation.

[0004] The technical solution of the present invention is: a method for analyzing the deformation of the measurement field of a large fixture under a non-uniform temperature field, including the following steps:

[0005] Step 1: Construction of the finite element model of the aircraft fixture:

[0006] 1-1 Use CAD software to establish an accurate three-dimensional geometric model of the aircraft fixture that is 1:1 with the physical object;

[0007] 1-2 Delete the bosses, triangular plates, gaskets, screws and bolts in the geometric model and then import it into the simulation software.

[0008] Step 2: Design of the measurement plan:

[0009] 2-1 Control the on-site environmental factors of the fixture: the temperature T is less than 40 degrees Celsius; the relative humidity < 85%; there is no vibration source within a range of 20m × 20m around the fixture;

[0010] Layout of measurement reference points: According to the span range of the tooling, divide the sub-regions at equal intervals, set reference points by height stratification within each sub-region, arrange temperature sensors on these reference points, and use a laser tracker for the next measurement;

[0011] Establish a multi-station tooling coordinate system and conduct measurements: Surround the tooling with multiple laser trackers, select four station-setting reference points on the tooling, measure the four station-setting reference points with multiple laser trackers, establish the tooling coordinate system of multiple laser trackers at this station, conduct m measurements on all reference points and record the coordinates and temperatures of each reference point in each measurement;

[0012] Obtain the unit temperature thermal deformation matrix: Calculate the unit temperature thermal deformation matrix according to Formula 1

[0013]

[0014] where is the difference between the average measured coordinate and the theoretical coordinate value of the i-th reference point in m measurements; P Ai is the theoretical coordinate of the i-th reference point; ΔT is the temperature difference.

[0015] Correct the random error of λ i : Calculate the corrected unit temperature thermal deformation matrix according to Formula 2

[0016]

[0017] where k is the number of measurements; λ i is the unit temperature thermal deformation coefficient matrix at the i-th temperature; λ S is the corrected unit temperature thermal deformation matrix.

[0018] Step 3 Finite element simulation calculation:

[0019] Set the material property parameters according to the tooling material, including: thermal conductivity, coefficient of thermal expansion, Young's modulus, Poisson's ratio, density;

[0020] Boundary condition setting: First set the ambient temperature, then split the tooling geometric model into different parts by sub-region, and assign the measured temperature of the reference points in the corresponding sub-region to the nodes in the corresponding geometric model;

[0021] Mesh generation: The maximum size of the mesh length, width, and height does not exceed 1% of the tooling length, width, and height;

[0022] Analysis of simulation results: Calculate the thermal deformation of the i-th point in the three coordinate directions of the model according to Formula 3

[0023]

[0024] where ΔL ix 、ΔL iy 、ΔL iz are the thermal deformations in the x, y, and z directions of any grid cell respectively; λ ix 、λ iy 、λ iz are the thermal deformation coefficients in the x, y, and z directions respectively; ΔT is the temperature difference; L x 、L y 、L z are the coordinate values of the point coordinates in the three directions respectively; for n observation points, the thermal deformation coefficient λ F of unit temperature is as shown in Formula 4;

[0025]

[0026] Step 4 Simulation model calibration:

[0027] 4-1: Correlation analysis of the thermal deformation matrix of unit temperature: Perform correlation analysis on the x, y, and z directions of λ F and λ S . Through matrix correlation coefficient calculation, it can be written as:

[0028] b = corrcoef(λ s , λ F )

[0029] In the formula, b is the correlation coefficient matrix; corrcoef is the matrix correlation coefficient calculation function in statistics; λ S is the corrected thermal deformation matrix of unit temperature obtained from experimental tests; λ F is the thermal deformation matrix of unit temperature obtained from finite element simulation; if each element (i.e., the correlation coefficient) in the b matrix satisfies b > 0.995 and b ≤ 1, it indicates that the calculation result of the finite element model at this point on the tooling meets the accuracy requirements. Then calculate and judge each point one by one until all points are judged. If the requirements are not met, the simulation model needs to be corrected;

[0030] 4-2: Simulation model correction: Increase the grid density in the simulation, and reduce the maximum size of the grid length, width, and height to not exceed 0.5% of the tooling length, width, and height. If the accuracy requirements of the tooling finite element model are still not met, the maximum size of the grid length, width, and height can be continuously reduced until the calculation meets the correlation requirements. Description of the drawings

[0031] Figure 1 is the finite element model of the aircraft tooling in Step 1 of the present invention

[0032] Figure 2Schematic diagram of sub-region division of the tooling for experimental measurement in Step 2 of the present invention

[0033] Figure 3 Simulation calculation results in Step 3 of the present invention

[0034] Figure 4 Flow chart of the present invention

[0035] Figure 5 Displacement along the height direction obtained by simulation in Step 4 of the present invention, as well as comparison between measurement results and simulation results

[0036] Explanation of numbers in the figure: 1. Large-scale tooling Detailed implementation manners

[0037] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0038] A method for measuring field deformation analysis under non-uniform temperature field of a large-scale tooling 1 includes the following steps:

[0039] Step 1, construction of the finite element model of the aircraft tooling

[0040] 1-1: Use CATIA R2018 software to establish an accurate 3D geometric model of the aircraft tooling that is 1:1 with the physical object

[0041] 1-2: After deleting the bosses, triangular plates, gaskets, screws and bolts in the geometric model, import it into the simulation software, as Figure 1 shown.

[0042] Step 2, measurement scheme design

[0043] 2-1: Control the on-site environmental factors of the tooling: Since the environment where the large-scale tooling 1 is located is complex and diverse, the complex environment will seriously affect the accuracy of the measured data. It is necessary to investigate the on-site environment of the tooling, and it is required that the on-site temperature T is less than 40 °C; the relative humidity < 85%; there is no vibration source within a range of 20 m × 20 m around the tooling

[0044] 2-2: Layout of measurement reference points: According to the span range of the tooling, divide the sub-regions at equal intervals of 10 m, as Figure 2 shown. Set reference points at a height interval of 1 m for each layer in each sub-region, arrange temperature sensors at these reference points, and use a laser tracker for the next measurement

[0045] 2-3: Establish the multi-station tooling coordinate system and conduct measurements: Set up 3 laser trackers around the tooling, select four benchmark points for station establishment on the tooling, and all 3 laser trackers measure the four benchmark points for station establishment to establish the tooling coordinate system of multiple laser trackers at this station. Conduct 5 measurements on all benchmark points and record the coordinates and temperatures of each benchmark point in each measurement;

[0046] 2-4: Obtain the unit temperature thermal deformation matrix: Calculate the unit temperature thermal deformation matrix according to Formula 1

[0047]

[0048] where is the difference between the average measured coordinate and the theoretical coordinate value of the i-th benchmark point (here, the second benchmark point is taken) under 5 measurements. Take P Ai as the theoretical coordinate of the second benchmark point (15710.31, 2764.27, 2793.79); ΔT is the temperature difference, and at this point, take ΔT = 2°C. Obtain λ2 = [0.00000614, 0.0000195, 0.0000272] T .

[0049] 2-5: Correct the random error of λ i : Calculate the corrected unit temperature thermal deformation matrix according to Formula 2

[0050]

[0051] where k is the number of measurements, take k = 5; λ i is the unit temperature thermal deformation coefficient matrix at the fifth temperature; λ S is the corrected unit temperature thermal deformation matrix. Calculate and obtain λ S = [0.00000614, 0.0000194, 0.0000272] T .

[0052] Step Three, finite element simulation calculation

[0053] 3-1: Set the material property parameters according to the tooling material, including: thermal conductivity of 60.5 W / (m·°C), thermal expansion coefficient of 1.2e-5 °C -1 , Young's modulus of 210 GPa, Poisson's ratio of 0.30, density of 7850 kg / m 3 .;

[0054] 3-2: Set the boundary conditions: First, set the ambient temperature T = 20°C, then split the tooling geometric model into 4 parts by sub-region, and assign the measured temperatures of the benchmark points in the corresponding sub-region to the nodes in the corresponding geometric model;

[0055] 3-3: Mesh generation: The maximum dimensions of the length, width, and height of the mesh shall not exceed 1% of the length, width, and height of the tooling.

[0056] 3-4: Analysis of simulation results: The simulation calculation is completed in the ABAQUS 6.14 software, and the calculation results are as Figure 3 shown. According to Equation 3, the thermal deformations in the three coordinate directions of the i-th point in the model are calculated

[0057]

[0058] where ΔL ix , ΔL iy , and ΔL iz are the thermal deformations in the x, y, and z directions of any mesh element, respectively; λ ix , λ iy , and λ iz are the thermal deformation coefficients in the x, y, and z directions, respectively. Take λ ix = λ iy = λ izz = 1.2e-5 °C -1 ; ΔT is the temperature difference, which is imported from the actual test results in 3-3; L x , L y , and L z are the coordinate values of the point coordinates in the three directions, respectively; thus, the thermal deformations in the x, y, and z directions are calculated. For the first 3 observation points, the thermal deformation coefficient per unit temperature λ F is as shown in Equation 4;

[0059]

[0060] Step 4, Calibration of the simulation model

[0061] 4-1: Correlation analysis of the thermal deformation matrix per unit temperature: Perform correlation analysis on the x, y, and z directions of λ F and λ S , and it can be written through the calculation of the matrix correlation coefficient as:

[0062] b = corrcoef(λ s , λ F )

[0063] In the formula, b is the correlation coefficient matrix; corrcoef is the matrix correlation coefficient calculation function in statistics, and this function is directly called from the R language library; λ S is the corrected thermal deformation matrix per unit temperature obtained from experimental tests; λ F is the thermal deformation matrix per unit temperature obtained from finite element simulation. After substituting, b = [1.0 1.0; 1.0 1.0] can be obtained for this measurement pointT , meeting the requirements of each element (i.e., the correlation coefficient) in the b matrix, that is, b > 0.995 and b ≤ 1, indicating that the comparison error between the measurement result and the simulation result at this point on the tooling can meet the engineering requirements, as Figure 5 shown. Then, calculate and discriminate each point one by one until all points are traversed and the process ends.

[0064] The above content is a further detailed description of the present invention in combination with specific preferred embodiments. It cannot be determined that the specific implementation of the present invention is only limited to these descriptions. For those of ordinary skill in the technical field to which the present invention pertains, without departing from the concept of the present invention, several simple deductions or substitutions can still be made, and all should be regarded as belonging to the protection scope of the present invention.

[0065] The parts not involved in the present invention are the same as the prior art or can be implemented by the prior art.

Claims

1. A method for measuring field deformation analysis under non-uniform temperature fields of large tooling, characterized in that, It includes the following steps: Step 1: Construction of the finite element model of the aircraft tooling; Step 2: Design of the measurement plan, including the following steps: a) Control the on-site environmental elements of the tooling: the temperature T is less than 40 °C; the relative humidity < 85%; there is no vibration source within a range of 20 m × 20 m around the tooling; b) Layout of the measurement reference points: According to the span range of the tooling, divide the sub-regions at equal intervals, set the reference points at different heights in each sub-region, arrange temperature sensors on these reference points, and use a laser tracker for the next measurement; c) Establish a multi-station tooling coordinate system and conduct measurements: Set multiple laser trackers around the tooling, select four station-building reference points on the tooling, and all multiple laser trackers measure the four station-building reference points, establish the tooling coordinate system of the multiple laser trackers at this station, conduct m measurements on all reference points, and record the coordinates and temperatures of each reference point in each measurement; d) Obtain the unit temperature thermal deformation matrix: Calculate the unit temperature thermal deformation matrix according to Formula 1 wherein is the difference between the mean of the measured coordinates of the i-th reference point under m measurements and the theoretical coordinate value; P Ai is the theoretical coordinate of the i-th reference point; ΔT is the temperature difference; e) Correction of λ i Random error: Calculate the corrected thermal deformation matrix per unit temperature according to Equation 2 where k is the number of measurements; λ i is the coefficient matrix of thermal deformation per unit temperature at the i-th temperature; λ S is the corrected coefficient matrix of thermal deformation per unit temperature; Step 3: Finite element simulation calculation, including the following steps: a) Set the material property parameters according to the tooling material, including: thermal conductivity, thermal expansion coefficient, Young's modulus, Poisson's ratio, density; b) Set the boundary conditions: First set the environmental temperature, then split the tooling geometric model into different parts according to the sub-regions, and assign the measured temperatures of the reference points in the corresponding sub-regions in the geometric model to the nodes in the corresponding geometric model; c) Mesh generation: The maximum size of the mesh length, width, and height does not exceed 1% of the length, width, and height of the tooling; d) Analysis of the simulation results: Calculate the thermal deformation of the i-th point in the model in the three coordinate directions according to Formula 3 where ΔL ix , ΔL iy , ΔL iz are the thermal deformations of any grid cell in the x, y, and z directions respectively; λ ix , λ iy , λ iz are the thermal deformation coefficients in the x, y, and z directions respectively; ΔT is the temperature difference; L x , L y , L z are the coordinate values of the point coordinates in the three directions respectively; for n observation points, the thermal deformation coefficient λ F is as shown in Equation 4; Step 4: Calibration of the simulation model.

2. The method for measuring field deformation analysis under non-uniform temperature fields of large tooling according to claim 1, characterized in that The specific process of the above-mentioned Step 1: Construction of the finite element model of the aircraft tooling is as follows: 2-1 Use CAD software to establish an accurate 1:1 three-dimensional geometric model of the aircraft tooling with the physical object; 2-2 Delete the bosses, triangular plates, gaskets, screws, and bolts in the geometric model and then import it into the simulation software.

3. The method for measuring field deformation analysis under non-uniform temperature fields of large tooling according to claim 1, characterized in that, Step 4: Calibration of the simulation model, including the following steps: 3-1 Correlation analysis of the thermal deformation matrix of unit temperature: For λ F and λ S perform correlation analysis in the x, y, and z directions respectively, and write it through the calculation of the matrix correlation coefficient as: b = corrcoef(λ s , λ F ) Where b is the correlation coefficient matrix; corrcoef is the matrix correlation coefficient calculation function in statistics; λ S is the modified unit temperature thermal deformation matrix obtained from experimental tests; λ F is the unit temperature thermal deformation matrix obtained from finite element simulation; if each element in the b matrix satisfies b > 0.995 and b ≤ 1, it indicates that the calculation result of the finite element model at this point on the tooling meets the accuracy requirements. Then, each point is calculated and judged one by one until all points are judged. If the requirements are not met, the simulation model needs to be corrected; 3-2 Modify the simulation model: Increase the mesh density in the simulation, reduce the maximum size of the mesh length, width, and height to not exceed 0.5% of the length, width, and height of the tooling. If the accuracy requirements of the tooling finite element model are still not met, continue to reduce the maximum size of the mesh length, width, and height until the calculation meets the correlation requirements.

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