Compensation method for thermal deformation of aviation large-size workpiece

Abstract

The invention relates to the technical field of precision machining, in particular to a compensation method for thermal deformation of an aviation large-size workpiece, which comprises the following steps of: firstly, establishing a first mapping relation between the size change of a calibration piece at different temperatures and the temperature through a thermal deformation calibration experiment; then, by taking the experimental data as a reference, correcting a thermal expansion coefficient in the calibration piece simulation model through an optimization algorithm, and establishing a high-precision prediction model for deformation of the workpiece to be machined; in the actual machining process, real-time temperature field data are collected through a temperature sensor arranged in a key area of a machine tool, and the thermal deformation error of a workpiece to be machined and the thermal offset of the original point of a machining coordinate system are predicted through the prediction model; and finally, according to a prediction result, a machining track is compensated in real time by dynamically offsetting a machining coordinate system and modifying the scaling ratio of each axis of a numerical control system. According to the method, the problem that under the non-constant-temperature working condition, machining is out of tolerance due to thermal deformation of the aviation large-size workpiece is effectively solved, and the machining precision and the percent of pass are remarkably improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of precision machining, and particularly relates to a compensation method for thermal deformation of an aviation large-size workpiece. BACKGROUND

[0002] In the field of aviation precision manufacturing, the machining precision of large-size workpieces (such as aircraft stringers, wall plates, web plates, etc.) directly affects the assembly quality and service performance of the whole machine structure. Such workpieces usually have an ultra-long structure (the length can reach 6-10 meters), and during the machining process, due to the dynamic change of the environmental temperature field, there is a temperature difference between the workpiece and the machining equipment, which causes thermal deformation of the workpiece, and further causes the machining feature size and the shape and position tolerance to be out of tolerance. This hidden error caused by thermal deformation not only interferes with the out-of-tolerance judgment in the manufacturing process, but also may cause the qualified parts to be misjudged as out-of-tolerance or the out-of-tolerance parts to be misjudged as qualified.

[0003] In the traditional process, in order to compensate for the thermal deformation error, the process personnel usually manually measure the error amount, and compensate by means of the scaling function of the numerical control system. However, since the thermal deformation is affected by many factors, the compensation logic is complex, the manual decision-making process is not only inefficient, but also prone to errors, and it is difficult to achieve accurate and dynamic error compensation.

[0004] In the prior art, there are some modeling and compensation methods for machine tool thermal errors. For example, Chinese patent CN119794885A discloses a numerical control machine tool thermal error compensation method and device considering temperature vibration coupling, which calculates the spindle temperature distribution by analyzing the spindle heat generation rate, and then calculates the error caused by the spindle thermal elongation; Chinese patent CN119623204A discloses a thermal error modeling method for large and medium-sized machine tool basic structures, which divides the machine tool as a whole into a plurality of finite element units, and arranges temperature sensors at key positions, and constructs a static thermal error model based on nodes to achieve compensation. However, the above-mentioned methods mainly aim at the thermal error of the machine tool itself, and do not involve the thermal deformation problem of the workpiece in the machining process.

[0005] In addition, Chinese patent CN110096760A discloses a numerical simulation method for workpiece thermal deformation, which divides the grid of the workpiece geometric model, establishes a time-dependent partial differential equation, and solves the displacement of the grid element vertex under the constraint conditions and boundary conditions. Although this method involves workpiece thermal deformation simulation, it does not combine the thermal deformation compensation strategy in the actual machining process design, and lacks the ability to achieve dynamic compensation in the machining process, thus having limitations in actual engineering application.

[0006] In summary, the existing technology lacks a systematic method for modeling and real-time compensation of thermal deformation of large-sized aerospace workpieces under non-constant temperature conditions. There is an urgent need to propose a technical solution that can dynamically predict and compensate for the thermal deformation of workpieces during the processing, so as to improve the accuracy and intelligence level of aerospace product manufacturing. Summary of the Invention

[0007] To address the shortcomings of existing technologies, this invention proposes a method for compensating for thermal deformation of large-sized aerospace workpieces. This method can accurately predict the problems of out-of-tolerance characteristic dimensions and geometric tolerances caused by thermal deformation when machining large-sized workpieces under non-constant temperature conditions, and can achieve dynamic and automated error compensation during the machining process, thereby improving machining accuracy.

[0008] To achieve the above objectives, the present invention adopts the following technical solution:

[0009] This invention proposes a method for compensating for thermal deformation of large-sized aerospace workpieces, comprising the following steps:

[0010] S1. By measuring the dimensional changes of the calibration part in a preset direction under different temperature gradients, a first mapping relationship between the thermal deformation of the experimental dimensions and temperature is established.

[0011] S2. Establish the finite element simulation model of the calibration component and obtain the second mapping relationship between the thermal error of the simulation dimensions and temperature; based on the difference between the first mapping relationship and the second mapping relationship, reconstruct the material thermal expansion coefficient model in the finite element simulation model of the calibration component, and correct the material thermal expansion coefficient model through an optimization algorithm to obtain the corrected thermal expansion coefficient model.

[0012] S3. Multiple temperature sensors are spaced out on the machine tool to collect temperature data of the processing environment in real time.

[0013] S4. Establish a finite element simulation model of the workpiece to be processed, and assign the modified thermal expansion coefficient model to the finite element simulation model of the workpiece to be processed to obtain a prediction model. Based on the collected temperature data, determine whether the current temperature field fluctuation is stable. If so, determine a representative temperature value according to the temperature data, substitute the representative temperature value into the prediction model, and predict the thermal deformation of the workpiece in each direction and the thermal offset of the origin of the processing coordinate system under the current processing conditions.

[0014] S5. Based on the predicted thermal deformation and thermal offset of the origin of the machining coordinate system, offset compensation is performed on the machining coordinate system of the workpiece to be machined, and scaling compensation is performed on the CNC machining commands.

[0015] Furthermore, the calibration component is made of the same material as the workpiece to be processed. In S4, the current processing temperature value is the average value of temperature data collected by multiple temperature sensors.

[0016] Furthermore, in S2, the model for the coefficient of thermal expansion is:

[0017]

[0018] In the formula θ is the coefficient of thermal expansion, m is the order, θ0, θ1, θ2, ..., θ m Let θ be the parameter vector to be optimized.

[0019] Furthermore, in S2, the optimization algorithm is an objective function established based on the least squares method, and the parameters of the thermal expansion coefficient model are iteratively updated using the gradient descent method.

[0020] Furthermore, the objective function is:

[0021]

[0022] In the formula, For temperature gradient T i The simulated dimensional change is given by N, where N is the total number of temperature gradients.

[0023] Furthermore, in S4, the specific method for determining whether the current temperature field fluctuation is stable is as follows: process the collected multiple temperature data, calculate their temperature mean and standard deviation, calculate the temperature tolerance range through the temperature mean and standard deviation, predict the size variation tolerance range corresponding to the temperature tolerance range using the finite element simulation model of the workpiece to be processed, calculate the process capability index based on the size tolerance range, and if the process capability index is greater than or equal to a set threshold, then the current temperature field fluctuation is determined to be stable.

[0024] Furthermore, in S1, after the calibration parts have reached thermal equilibrium under different temperature gradients, dimensional measurements are performed. The time t required for thermal equilibrium is:

[0025]

[0026] In the formula, L0 is half the maximum length of the calibration part. The thermal diffusivity of the material.

[0027] Furthermore, in S5, compensation for the machining coordinate system is achieved by adding a thermal offset to the origin of the machining coordinate system.

[0028] Furthermore, in S5, the scaling compensation process for CNC commands is as follows: based on the predicted thermal deformation, the scaling ratio of the workpiece to be processed in each direction is calculated, and the CNC machining commands are scaled and compensated according to the calculated scaling ratio.

[0029] The present invention also proposes a computer-readable storage medium having a computer program stored thereon, characterized in that the computer program, when executed by a processor, implements the steps of the above-described method.

[0030] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0031] (1) Existing thermal error compensation technologies mainly target the machine tool body, while this invention constructs a precise prediction and compensation system for thermal deformation of large-sized aerospace workpieces. By establishing a precise mapping relationship between the workpiece temperature field and deformation field, the problem of machining deviation caused by workpiece thermal deformation is directly solved. Real material thermal deformation data are obtained through experiments, and then the parameters are precisely corrected using a simulation model. This dual verification mechanism effectively overcomes the limitations of relying solely on simulation or experience, and is especially suitable for aerospace components with complex material properties and unusual dimensions.

[0032] (2) This invention solves the positioning error caused by the overall expansion of the workpiece by coordinate system offset compensation, and solves the dimensional error caused by anisotropic deformation by proportional scaling compensation. This refined compensation strategy overcomes the shortcomings of the traditional single proportional scaling method.

[0033] (3) This invention introduces the process capability index as a quantitative evaluation standard for temperature field stability, requiring the process capability index in all monitoring directions to simultaneously meet the stringent standards. This multi-dimensional and quantitative evaluation method ensures the reliability of the input data of the prediction model, guarantees the compensation accuracy from the source, and avoids miscompensation caused by local temperature anomalies.

[0034] (4) The present invention achieves full automation of the entire process from temperature data acquisition and thermal deformation prediction to G-code modification, and is applicable to workpieces of various geometries without the need for manual intervention. The application of the edge computing controller ensures the real-time nature of the compensation, and can dynamically respond to temperature changes during the processing, which greatly improves production efficiency and reduces the dependence on the technical level of the operators. Attached Figure Description

[0035] Figure 1 This is an overall flowchart of the compensation method of the present invention;

[0036] Figure 2 The diagram shows the installation of temperature sensors; (a) is a diagram showing the temperature sensor installed on the left side wall of the spindle; (b) is a diagram showing the temperature sensor installed on the right side wall of the spindle; (c) is a diagram showing the temperature sensor installed on the rear side wall of the spindle; (d) is a diagram showing the temperature sensor installed on the side wall of the spindle box; (e) is a diagram showing the temperature sensor installed on the outside of the spindle; and (f) is a diagram showing the temperature sensor installed on the outside of the machine tool.

[0037] Figure 3Visualize the thermal deformation results of the workpiece;

[0038] Figure 4 This is the result of machining coordinate system offset and workpiece dimensional deformation. Detailed Implementation

[0039] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0040] Example

[0041] refer to Figure 1 This embodiment proposes a method for compensating for thermal deformation of large-sized aerospace workpieces, which is performed according to the following steps:

[0042] S1. Heat deformation calibration, which shall be performed according to the following sub-steps:

[0043] S101. Select a calibration component. The material of the calibration component is the same as that of the workpiece to be processed, and its geometric properties are also related to the thermal deformation behavior of the workpiece to be processed, so as to ensure that the thermal expansion coefficient model obtained through its calibration can be used to predict the thermal deformation of the workpiece to be processed during the processing. Specifically, the calibration component can be designed in one of the following forms:

[0044] a) A geometrically similar scaled-down model of the workpiece to be processed; for example, when the workpiece to be processed is an aircraft stringer, the calibration part can be a model of the same material but with its length and cross-sectional shape scaled down. This model retains the "T" or "L" shaped cross-sectional features of the stringer, thereby simulating the thermal expansion and bending trends of the actual workpiece in different directions.

[0045] b) A representative segment cut from the workpiece to be processed, or a simulated segment containing at least one feature to be processed on the workpiece to be processed; for example, when the workpiece to be processed is a large panel, the calibration piece can be a representative segment cut from the same plate, containing a typical reinforcing rib and a connecting hole. By calibrating the thermal deformation of the hole position and rib spacing on the segment, it can be directly used to correct the processing compensation of similar features on the panel.

[0046] c) is a regular geometric body, such as a cuboid or a cylinder, which has characteristic dimensions in at least two different directions. For example, when the workpiece to be processed is a flat plate, the calibration part can be a cuboid, and preferably the length, width, and height of the calibration part are the same as those of the workpiece to be processed.

[0047] S102. Select a reference temperature. In this embodiment, the reference temperature is selected as 20℃. At the reference temperature, a coordinate measuring machine is used to measure the dimensions of the calibration part in the critical directions. The largest dimension is selected as the initial reference dimension from the measured dimensions. In actual operation, the selection of the initial reference dimension can also be determined according to the requirements. The change in dimensions in the critical directions can characterize the thermal deformation behavior of the calibration part. The critical directions must include at least two orthogonal coordinate axes. For example, the critical directions include two directions: the X-axis and the Y-axis. Or, the critical directions include three directions: the X-axis, the Y-axis, and the Z-axis. In this embodiment, the workpiece to be processed is a flat plate component (cubic prism). The calibration part is a cuboid with the same dimensions as the workpiece to be processed. For the cuboid workpiece to be processed, the critical directions are the X-axis, Y-axis, and Z-axis. That is, its length L needs to be measured at 20℃. x0 Width L y0 Height L z0 In L x0 L y0 L z0 The maximum value is selected as the initial reference size. For example, in this embodiment, L x0 >L y0 >L z0 Then choose to use L x0 Used as the initial reference dimension.

[0048] S103. Simulate the actual processing temperature range, for example, 15~30℃, and set N temperature gradients T at certain temperature intervals (e.g., 1℃). i (i=1, 2, ..., N); Allow the calibration piece to stand at each temperature gradient until it reaches thermal equilibrium. Then, using the same measuring tool, measure the dimension L of the calibration piece at the current temperature gradient in the direction of the initial reference dimension. xi In actual operation, if there are more than two maximum dimensions, then choose one of the directions of the maximum dimension. For example, L x0 =L y0 >L z0 Therefore, the initial reference dimension can be located either in the X-axis or Y-axis direction. In this step, the time t required for thermal equilibrium is:

[0049]

[0050] In the formula, L0 is half the maximum length of the calibration part. The thermal diffusivity of the material.

[0051] S104. Calculate the thermal deformation of the calibration part in the direction of the initial reference dimension under each temperature gradient:

[0052]

[0053] Establish the first mapping relationship between the thermal deformation of the experimental dimensions and temperature, i.e. , For temperature gradient T i The experimental size change.

[0054] S2. Correct the material thermal expansion coefficient model based on the calibration results of S1, specifically by following these sub-steps:

[0055] S201. Import the 3D CAD model of the calibration part into the finite element analysis software and perform automatic mesh generation;

[0056] Define the initial properties of the calibration component material, including elastic modulus, Poisson's ratio, thermal conductivity, specific heat capacity, and an initial thermal expansion coefficient model, which can be a constant value (θ0) or a first-order linear model (θ0+θ1T).

[0057] For each temperature gradient, a thermal boundary condition (uniform temperature field) is applied. Since the thermal deformation of the material is linear elastic with small displacement, and the boundary condition remains almost unchanged during loading, a linear static analysis is performed to calculate the displacement field caused by thermal strain.

[0058] From the simulation results, the dimensional thermal error corresponding to the measurement direction in S103 is extracted. In this step, the reference temperature is the same as in S102, and the simulated dimensional thermal error under each temperature gradient is obtained. This establishes the second mapping relationship in the simulation, namely .

[0059] S202. Constructing a material thermal expansion coefficient model: The material thermal expansion coefficient model is defined as a nonlinear function related to temperature T. In this embodiment, a polynomial model is used.

[0060]

[0061] In the formula is the coefficient of thermal expansion, m is the order of the polynomial, 3≤m≤5 and m is an integer; in this embodiment, m=3 is taken.

[0062] The multidimensional parameters to be optimized are a vector θ. .

[0063] In the finite element simulation model, it is assumed that the thermal deformation of the part is linear, and the initial thermal expansion coefficient model in the finite element simulation model can be a constant value or a first-order linear model. However, in reality, due to the non-uniformity of the material, the actual thermal expansion coefficient may have a non-linear relationship with temperature. Especially for large-sized parts, the change in thermal expansion coefficient leads to a more obvious difference between thermal deformation and theoretical deformation. Therefore, the initial thermal expansion coefficient model is replaced with the constructed material thermal expansion coefficient model, and the constructed material thermal expansion coefficient model is optimized.

[0064] S203. Establish an objective function based on the least squares method. The objective function is the weighted mean square error of the error in the measurement direction, and its expression is:

[0065]

[0066] In the formula, For temperature gradient T i The simulation shows the dimensional change; the multidimensional parameter θ is optimized to find the optimal parameter θ. opt , making Minimum.

[0067] S204. The gradient descent method is used to iteratively update the material's thermal expansion coefficient model. Since the finite element simulation cannot be directly differentiated, the central difference method is used for numerical calculation. For parameter θ j Gradient of (j=0,1,2,…,m) .

[0068] Then press Update the parameters, where η is the learning rate, until the convergence condition (MES) is met. total (At a preset threshold) or after reaching the maximum number of iterations, a high-precision corrected thermal expansion coefficient model is obtained.

[0069] S3. Temperature field acquisition under actual machining conditions: Multiple temperature sensors (such as PT100) are installed on the machine tool. (Reference) Figure 2 In this embodiment, the temperature sensor is installed on the left side wall of the spindle (e.g., Figure 2 (a) The right side wall of the main shaft (e.g.) Figure 2 (b)) Rear sidewall of the main shaft (e.g. Figure 2 (c) Spindle box sidewall (e.g. Figure 2 (d) The position on the outside of the spindle, about 3~5cm away from the spindle (e.g. Figure 2 (e) The outer edge of the machine tool is about 3-5cm away from the machine tool (e.g. Figure 2 (f) The temperature values ​​measured by each sensor are transmitted to the edge computing controller via a wireless transmitter and stored in chronological order.

[0070] S4. Simulation prediction of thermal deformation of the workpiece under current machining conditions:

[0071] S401. Based on the three-dimensional CAD model of the workpiece to be processed, establish a finite element simulation model of the workpiece to be processed, and assign the modified thermal expansion coefficient model to the finite element simulation model of the workpiece to be processed to obtain a prediction model.

[0072] S402. Calculate the average temperature based on the real-time temperature data collected by the edge computing controller. and standard deviation :

[0073]

[0074] M represents the total number of temperature sensors, T j Let be the temperature value of the j-th temperature sensor.

[0075]

[0076] S403. Determine whether the current temperature field fluctuation is stable. The determination method is: through the temperature average. and standard deviation Calculate the temperature tolerance range The size variation deviation interval corresponding to the upper and lower limits of the interval is calculated using the prediction model, and the process capability index is calculated using the size variation deviation interval. , If the temperature field fluctuation is stable, the average temperature will be set. The temperature value is used as the representative temperature value of the current temperature field and is entered into S404; otherwise, the temperature sensor layout should be adjusted or the temperature sensor should be checked for proper functioning.

[0077] In this step, the upper and lower limits of the temperature tolerance range correspond to the coefficients of thermal expansion at the corresponding temperatures. , :

[0078]

[0079] Size variation range The calculation method is as follows:

[0080]

[0081] Process capability index The calculation method is as follows:

[0082]

[0083] S404, will Substituting the values ​​into the prediction model and running the finite element simulation, the displacement field at each position of the workpiece to be processed can be obtained. Post-processing can then extract the thermal deformation of the workpiece in the X, Y, and Z axes from the displacement field. and the thermal offset of the origin of the machining coordinate system , The visualization results are as follows Figure 3 As shown.

[0084] S5. During the machining process, the main manifestations of thermal error are thermal offset of the machining coordinate system and thermal deformation of the features. Taking multiple groove features as an example, such as... Figure 4 As shown, the former is due to the thermal expansion of the workpiece, which causes the machining coordinate system established based on the theoretical workpiece model to deviate from the actual position; the latter is due to the thermal expansion of the workpiece, which causes the machining dimensions of the workpiece to be inconsistent with the design dimensions.

[0085] S501. Compensation for thermal offset of the machining coordinate system: based on the predicted thermal offset of the machining coordinate system origin. For the origin of the original machining coordinate system Make corrections:

[0086]

[0087] This is the origin of the corrected machining coordinate system.

[0088] This operation is achieved by modifying the coordinate system offset parameters (such as G54) in the CNC system.

[0089] S502. For compensation of thermal deformation during feature machining: Calculate the scaling ratio of each axis:

[0090]

[0091] Sx, Sy, and Sz are the scaling ratios of the workpiece to be processed in the X-axis, Y-axis, and Z-axis directions, respectively. These are the dimensions of the workpiece to be processed in the X, Y, and Z axes at the reference temperature (20℃);

[0092] This operation uses the scaling instructions of the CNC system for correction. For example, the scaling instructions for the FANUC 0i CNC system are G50 / G51, including same-scale scaling: all axes are scaled at the same ratio (G51 X_Y_Z_P_, where P is the scaling factor) and different-scale scaling: each axis is set with an independent scaling ratio (G51 X_Y_Z_I_J_K_, where I, J, and K are the scaling factors for each axis); the scaling instructions for the Siemens CNC system are SCALE and ASCALE.

[0093] S503, calculate the origin thermal offset. The scaling ratios Sx, Sy, and Sz of each axis are input to the edge computing controller. The automatic compensation logic in the edge computing controller modifies the CNC machining program to achieve dynamic compensation. This logic includes the following functional modules:

[0094] Data input interface module: Receives origin thermal offset. and the scaling ratios of each axis: Sx, Sy, Sz;

[0095] CNC code parsing and positioning module: reads and positions the coordinate system (such as G54) and scaling (such as G51) instruction positions in the original G code.

[0096] Compensation instruction generation module: Generates new CNC instructions based on compensation parameters (such as updated G54 coordinates and scaling ratios of each G51 axis).

[0097] Code refactoring and output module: Writes new instructions into G-code files and sends them to the CNC machine tool.

[0098] The specific embodiments of the present invention are provided to enable those skilled in the art to understand or implement the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention.

[0099] It should be understood that the present invention is not limited to the content already described above, and various modifications and changes can be made without departing from its scope. The scope of the present invention is limited only by the appended claims.

Claims

1. A method for compensating for thermal deformation of large-sized aerospace workpieces, characterized in that, Includes the following steps: S1. By measuring the dimensional changes of the calibration part in a preset direction under different temperature gradients, a first mapping relationship between the thermal deformation of the experimental dimensions and temperature is established. S2. Establish the finite element simulation model of the calibration component and obtain the second mapping relationship between the thermal error of the simulation dimensions and temperature. Based on the difference between the first mapping relationship and the second mapping relationship, the material thermal expansion coefficient model in the finite element simulation model of the calibration component is reconstructed, and the material thermal expansion coefficient model is corrected by the optimization algorithm to obtain the corrected thermal expansion coefficient model. S3. Multiple temperature sensors are spaced out on the machine tool to collect temperature data of the processing environment in real time. S4. Establish a finite element simulation model of the workpiece to be processed, and assign the modified thermal expansion coefficient model to the finite element simulation model of the workpiece to be processed to obtain a prediction model. Based on the collected temperature data, determine whether the current temperature field fluctuation is stable. If so, determine a representative temperature value according to the temperature data, substitute the representative temperature value into the prediction model, and predict the thermal deformation of the workpiece in each direction and the thermal offset of the origin of the processing coordinate system under the current processing conditions. S5. Based on the predicted thermal deformation and thermal offset of the origin of the machining coordinate system, offset compensation is performed on the machining coordinate system of the workpiece to be machined, and scaling compensation is performed on the CNC machining commands.

2. The method for compensating for thermal deformation of large-size aerospace workpieces according to claim 1, characterized in that, The calibration component is made of the same material as the workpiece to be processed. In S4, the current processing temperature value is the average value of the temperature data collected by multiple temperature sensors.

3. The method for compensating for thermal deformation of large-size aerospace workpieces according to claim 1, characterized in that, In S2, the thermal expansion coefficient model is: In the formula, θ is the coefficient of thermal expansion, m is the order, θ0, θ1, θ2, ..., θ m Let θ be the parameter vector to be optimized.

4. The method for compensating for thermal deformation of large-size aerospace workpieces according to claim 1, characterized in that, In S2, the optimization algorithm is an objective function established based on the least squares method, and the parameters of the thermal expansion coefficient model are iteratively updated using the gradient descent method.

5. The method for compensating for thermal deformation of large-size aerospace workpieces according to claim 4, characterized in that, The objective function is: In the formula, For temperature gradient T i The simulated dimensional change is given by N, where N is the total number of temperature gradients.

6. The method for compensating for thermal deformation of large-size aerospace workpieces according to claim 1, characterized in that, In S4, the specific method for determining whether the current temperature field fluctuation is stable is as follows: process multiple collected temperature data, calculate their temperature mean and standard deviation, calculate the temperature tolerance range through the temperature mean and standard deviation, predict the size variation tolerance range corresponding to the temperature tolerance range using the finite element simulation model of the workpiece to be processed, calculate the process capability index based on the size tolerance range, and if the process capability index is greater than or equal to a set threshold, then the current temperature field fluctuation is determined to be stable.

7. The method for compensating for thermal deformation of large-size aerospace workpieces according to claim 1, characterized in that, In S1, after the calibration parts reach thermal equilibrium under different temperature gradients, dimensional measurements are performed. The time t required for thermal equilibrium is: In the formula, L0 is half the maximum length of the calibration part. The thermal diffusivity of the material.

8. The method for compensating for thermal deformation of large-size aerospace workpieces according to claim 1, characterized in that, In S5, compensation for the machining coordinate system is achieved by adding a thermal offset to the origin of the machining coordinate system.

9. The method for compensating for thermal deformation of large-size aerospace workpieces according to claim 1, characterized in that, In S5, the scaling compensation process for CNC commands is as follows: based on the predicted thermal deformation, the scaling ratio of the workpiece in each direction is calculated, and the CNC machining commands are scaled and compensated according to the calculated scaling ratio.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method as described in any one of claims 1 to 9.

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