A mechanism data double-driven tool deflection deformation compensation method for machining of complex thin-walled parts

Abstract

A kind of mechanism data double-driven complex thin-walled part machining let knife deformation compensation method.Acquire the actual contour of workpiece and wall thickness information, biasing solution actual inner surface along wall thickness direction;Considering the coupling effect of compensation amount and let knife deformation, a deformation compensation mechanism model is established in machining, and the compensation flexibility correction coefficient is solved;Based on BP neural network prediction model, with machining data as training set, the wall thickness compensation value is predicted;With the product of compensation flexibility coefficient and target wall thickness, the average value of wall thickness prediction compensation value is taken as the actual wall thickness compensation value, and the actual compensation tool position is solved by biasing along the wall thickness normal vector outward;With the normal vector and three-dimensional coordinates of tool position as input, generate NC machining code, complete complex thin-walled part let knife deformation compensation.The present application proposes the concept of compensation flexibility coefficient, proposes a compensation method driven by mechanism and data in view of the limitations of single method, solves the compensation tool position and completes digital processing, and realizes automation in the whole process and improves processing efficiency and precision.

Description

Technical Field

[0001] This invention belongs to the field of machining deformation compensation, and relates to a method for compensating for tool deflection deformation in the machining of complex thin-walled parts driven by both mechanism and data. Background Technology

[0002] With the development of my country's aerospace industry, higher requirements have been placed on the lightweighting and structural strength of its key components. For example, rocket propellant tank bottoms and common-base components are characterized by large geometric dimensions, low structural strength, complex surface shapes, and difficult-to-machine materials, making them highly susceptible to significant deformation during semi-finishing and finishing stages. The challenge of compensation machining stems from the deformation problem of complex thin-walled parts, including deformation from complex blank manufacturing, clamping deformation, deformation caused by the part's own weight, and deformation from subsequent machining. Directly compensating for the difference in wall thickness from the theoretical design model cannot guarantee the required accuracy of the remaining wall thickness.

[0003] Currently, there are two main types of tool deformation compensation methods: (1) establishing a cutting mechanism model for tool deformation and compensating based on the analytical values ​​of the model; in actual machining, tool deformation is affected by multiple factors, and the analytical model cannot fully consider the factors of the actual working conditions, resulting in a deviation between the analytical values ​​of deformation and the actual tool deformation; (2) making predictions based on multi-round machining data and combined with deep learning. Although this method combines the actual working conditions on site, it uses a pure data-driven approach to predict compensation values ​​and does not consider the tool deformation caused by structural changes during the material removal process of thin-walled parts, resulting in poor local accuracy of the predicted values. Therefore, a mechanism-data dual-driven tool deformation compensation method for complex thin-walled parts is proposed. In the mechanism part, the concept of compensation compliance coefficient based on the measured model is proposed. Combined with the established deep learning prediction model, the mechanism model is improved while its defects are complemented. Finally, the compensation tool position is calculated to achieve accurate compensation of tool deformation and ensure the machining accuracy requirements of complex thin-walled parts.

[0004] In 2014, Wei Zhaocheng et al. from Dalian University of Technology disclosed a method for compensating for tool deflection error in free contour surface milling in patent CN101791770B. This method compensates for the error by calculating the tool contact angle and the normal vector of each discrete node position during machining, and then offsetting the tool trajectory equidistantly along the normal direction. However, this method only considers the influence of the residual cutting height on tool deflection deformation, neglecting the influence of tool position deviation introduced by changes in the overall workpiece surface shape. In 2021, Peng Fangyu et al. from Huazhong University of Science and Technology disclosed a method for establishing a prediction model for tool deflection deformation error in thin-walled parts and its application in patent CN112668227B. This method establishes a cutting force model through finite element analysis and a small-sample learning model based on a neural network, predicting tool deflection deformation error based on the cutting force. This method considers the influence of process parameters on tool deflection deformation but ignores the influence of time-varying stiffness and surface shape deviation on local deformation during workpiece machining. In 2022, Feng Shunxiao et al. of Sichuan Aerospace Changzheng Equipment Manufacturing Co., Ltd. disclosed a method for compensating for the thickness error of a large thin-walled shell mesh skin in patent CN113894334A. This method groups the processing area based on mesh deformation tolerance and controls the shell wall thickness deformation through multiple rounds of measurement and iterative compensation. However, this method relies entirely on manual multi-round adjustments to ensure the final wall thickness accuracy, has a long processing cycle, and does not control the tool deformation error from the perspective of deformation mechanism.

[0005] Currently, no method for compensating for tool deflection deformation in complex thin-walled parts driven by both mechanistic data has been proposed. Summary of the Invention

[0006] The main technical problem addressed by this invention is to overcome the shortcomings of existing processes. Addressing the difficulties of controlling the wall thickness accuracy of complex thin-walled parts, complex surface details, and the time-consuming and inefficient manual adjustments in multiple rounds, this invention proposes a mechanism- and data-driven method for compensating for tool deformation during the machining of complex thin-walled parts. This method uses on-machine measurement via line laser and electromagnetic ultrasonic methods to acquire the actual outer profile and wall thickness information of the workpiece, and solves for the actual inner surface by offsetting along the wall thickness direction. Considering the coupling effect between the compensation amount and tool deformation, a deformation compensation mechanism model is established during machining, and the compensation compliance correction coefficient is solved. Based on a BP neural network prediction model, using multi-round historical machining data as a training set, the wall thickness compensation value is predicted. The product of the compensation compliance coefficient and the target wall thickness is averaged with the predicted wall thickness compensation value to obtain the actual wall thickness compensation value. This value is then offset outward along the wall thickness normal vector to solve for the actual compensation tool position. Using the normal vector and three-dimensional coordinates of the tool position as input, CNC machining code is generated to complete the tool deformation compensation for complex thin-walled parts.

[0007] The technical solution of this invention:

[0008] A mechanism- and data-driven method for compensating for tool deflection deformation in the machining of complex thin-walled parts is proposed. First, based on the surface features of the workpiece, a contour measurement trajectory is planned according to a theoretical model, and a wall thickness measurement trajectory is planned based on the measured contour, achieving on-machine scanning automatic measurement of the workpiece contour and wall thickness. Second, based on local surface measurement points, the normal vector is solved, and combined with the wall thickness measurement data, the actual internal surface point cloud is solved by inward bias. Then, a tool deflection deformation mechanism and compensation model are established. Based on multiple rounds of on-machine measurement data, the wall thickness compensation compliance correction coefficient is solved. Combined with a BP neural network model, using historical machining data of the same model as the training set, and taking the target wall thickness and measured wall thickness as input conditions, the compensation amount of the part to be machined is predicted. The average of the predicted values ​​from the mechanism model and the neural network is taken as the actual tool deflection deformation compensation amount. Finally, the compensation tool position point is used to generate machining code according to CNC machining instruction rules to complete the wall thickness tool deflection deformation compensation for complex thin-walled parts. The specific steps are as follows:

[0009] The first step is to solve for the actual internal shape of the workpiece based on the on-machine measurement data.

[0010] Taking into account both the machine tool travel and the actual dimensions of the workpiece, and under the premise that the sensor and workpiece do not interfere with each other and the measurement range is not exceeded, an on-machine measurement trajectory is planned. The actual profile information p of the workpiece is then acquired through an external communication method. i (x i ,y i ,z i A i C i ), i≤m, where m is the total number of profile sampling points; based on the actual profile, plan the electromagnetic ultrasonic thickness measurement trajectory and collect the workpiece wall thickness information q. j (x j ,y j ,z j A j C j ,d j ), j≤n, where n is the total number of wall thickness sampling points; the total number of profile sampling points m is much greater than n. Using the Kd-tree neighborhood search algorithm, the wall thickness information is matched with the profile information to obtain the wall thickness value corresponding to each point of the actual profile, denoted as p. i (x i ,y i ,z i A i C i ,d i );

[0011] The neighborhood radius is set based on the sampled point cloud density. Within the neighborhood radius, the PCA point cloud normal vector estimation method is used to estimate the plane using nearest neighbor points. By minimizing the objective function, p i The dot product of the vector formed by its nearest neighbors and the normal vector is zero.

[0012]

[0013] Where r is the number of points in the neighborhood, and c is the center point of the neighborhood; let S is a 3x3 covariance matrix. The normal vector is obtained by finding the eigenvector with the smallest eigenvalue of the covariance matrix. The solution;

[0014] p i The point is offset inward along the normal vector to the corresponding thickness d i The distance, i.e., obtaining the point cloud data p of the actual internal surface. i (x i ,y i ,z i A i C i ,d i ):

[0015]

[0016] Where x′, y′ ,z ′ represents the three-dimensional coordinates of the actual internal surface;

[0017] The second step is to establish a model of the tool deformation mechanism and solve for the compensation compliance coefficient.

[0018] When the clamping system is stable, the wall thickness deviation during machining is mainly caused by the deflection and tool deformation resulting from the coupling effect of the tool-workpiece system. This error is denoted as δ. d If the feed rate and spindle speed remain constant during the machining process, then δ d Represented as:

[0019] δ d =k′d f (3)

[0020] Where k′ is the compensation compliance coefficient, d f This represents the actual cutting depth.

[0021] According to the calculation theory of thin-walled shells, the formula for calculating the radial deflection deformation of a thin-walled shell micro-element is:

[0022]

[0023] Where F is the radial milling force of the micro-element, and E, h, μ are the elastic modulus, remaining wall thickness and Poisson's ratio of the thin-walled part, respectively.

[0024] The milling force F is related to the actual depth of cut, spindle speed, and the properties of the material being machined. Its calculation formula is as follows:

[0025] F = k * d f*z t *n (5)

[0026] Where k is the cutting force coefficient, z t Where n is the feed per tooth and n is the spindle speed.

[0027] Substituting equations (5) and (3) into equation (4), we obtain the compensation compliance coefficient k′ as follows:

[0028]

[0029] The workpiece profile changes after each machining cycle; therefore, the prediction of the compensation compliance coefficient considers the corresponding point M1 on the inner profile. The theoretical wall thickness for each machining cycle is h. 1,w w = 1,...,N; the actual wall thickness for each processing round is h. i1,w The compensation compliance coefficient for each round of processing is k′ 1,w The actual cutting depth in each round of machining is d. f1,w ;

[0030] The compensation compliance coefficient is closely related to the remaining wall thickness of the workpiece. Based on actual cutting data, the compensation compliance coefficient for subsequent machining processes is predicted using polynomial interpolation. Therefore, the compensation compliance coefficient k′ for the (N+1)th round is... 1,N+1 for:

[0031]

[0032] Due to the coupling effect between the compensation amount and the cutting feed rate, the machining error δ d1,N+1 With the actual compensation amount c 1,N+1 They are not equal. To ensure wall thickness accuracy, the sum of the actual compensation and deformation is 0, resulting in the following equation:

[0033] k′ 1,N+1 ·(h i1,N -h 1,N+1 +c 1,N+1 )-c 1,N+1 =0 (8)

[0034] That is, the actual compensation amount c can be obtained. 1,N+1 The calculation formula is:

[0035]

[0036] The third step is to predict the actual wall thickness compensation amount based on a BP neural network regression model.

[0037] During the machining of complex thin-walled parts, various conditions such as the machining environment and tool condition can affect the actual compensation value, causing deviations from the calculated value by the mechanistic model. To achieve precise control of tool deformation in complex thin-walled parts, a BP neural network regression prediction model is used to predict the actual deformation compensation value, which complements the predicted value of the mechanistic model, thereby ensuring the final wall thickness accuracy.

[0038] First, the deformation influence factor is determined to be the actual wall thickness h. i1,w Theoretical processing wall thickness h 1,w Spindle speed n, feed per tooth z t The input dataset is then represented as X = {x} (1) ,x (2) ,…,x (l)}, where l is the number of samples in the training dataset, x (i) The feature vector representing historical processed data is denoted as: Secondly, by removing the dimensions and orders of magnitude differences of different input units, the mean squared error of the input dataset is made relatively small, thus improving the convergence speed. The BP neural network regression prediction model consists of an input layer, hidden layers, and an output layer, and the final output model is expressed as:

[0039]

[0040] Among them, W (1) W (2) ,b (1) ,b (2) These represent the weights and biases between the input layer and the hidden layer, and between the hidden layer and the output layer, respectively. (1) Z (2) A represents the input to the hidden layer and the output layer, respectively. (1) The output of the hidden layer, v() is the output of the model, and v is the non-linear activation function.

[0041] The non-linear activation function used is the Sigmoid function, which is calculated as follows:

[0042]

[0043] Where 'a' is the input independent variable;

[0044] Finally, the parameters are updated along the direction of fastest descent of the error function using the backpropagation algorithm to establish an accurate solution model. A partial dataset is used as a test set to verify the BP neural network regression prediction model. Finally, the current processing data is used as input to predict the compensation amount c′ for the next round of processing. 1,N+1 ;

[0045] The fourth step is to generate compensation tool points based on the mechanism and data-driven wall thickness compensation values.

[0046] The compensation value c calculated based on the second step of the mechanism analysis model. 1,N+1 and the compensation value c′ predicted by the third step BP neural network regression model. 1,N+1 Calculate the average of the predicted values ​​for the corresponding points and use it as the final compensation value. The calculation formula is as follows:

[0047]

[0048] Based on the compensation values ​​calculated at each point in the final solution Combining the actual wall thickness value and the target wall thickness value d at each point ti For each point on the actual inner contour, offset outward along the normal direction to obtain the compensated machining tool position point. The formula for solving the tool position point is:

[0049]

[0050] Where, x tool ,y tool ,z tool The coordinates of the compensation tool point are X, Y, Z.

[0051] Finally, based on the position coordinates and normal vector of the compensation tool point, the compensation machining CNC code is generated. For complex thin-walled parts, multiple rounds of thinning machining are performed. In the roughing stage, a large amount of material is removed by milling according to the theoretical toolpath. Starting from the semi-finishing stage, the work of the second to fourth steps is repeated. This can realize the compensation of tool deformation for complex thin-walled parts driven by both mechanism data, achieve precise control of wall thickness, and meet the actual machining requirements.

[0052] The beneficial effects of this invention are as follows: This invention proposes a mechanism-data-driven method for compensating for tool deflection deformation in complex thin-walled parts. Based on an on-machine scanning measurement method and using an external control console, it achieves automated measurement of the part's profile and wall thickness data. Combined with the wall thickness data, it solves the actual inner profile point cloud data, establishing a mechanism model for tool deflection deformation during the machining process of complex thin-walled parts. A prediction model is established by integrating historical multi-round machining data of the same type of thin-walled part to obtain the final compensation value and generate the final CNC machining program. This solves the problems of low machining efficiency, difficulty in guaranteeing wall thickness accuracy, and low automation in the machining of complex thin-walled parts. The method described in this invention is simple to operate, highly efficient, fully automated, and highly reliable, meeting the requirements for wall thickness accuracy control in the actual machining of complex thin-walled parts. Attached Figure Description

[0053] Figure 1 This is a flowchart of the mechanism data dual-drive method for compensating for tool deformation in complex thin-walled parts as described in this invention.

[0054] Figure 2This is a schematic diagram for solving the point cloud of the actual inner surface from the actual outer profile and wall thickness.

[0055] Figure 3 This is a schematic diagram showing the deformation of the cutting tool at a certain point during the machining process.

[0056] Figure 4 A schematic diagram illustrating the relationship between the compensation compliance coefficient and the remaining wall thickness of the workpiece.

[0057] Figure 5 This is a schematic diagram of a BP neural network regression prediction model.

[0058] Figure 6 This is a schematic diagram of the process of generating the compensation tool point.

[0059] In the figure: 1. External operating platform; 2. Linear laser profile measurement sensor; 3. Electromagnetic ultrasonic wall thickness measurement sensor; 4. Actual shape surface point cloud; 5. Shape surface corresponding normal vector; d i 6. Actual wall thickness; 7. Actual internal surface point cloud; 8. Actual internal surface; 9. Target surface; 10. Actual machined surface; 11. Actual external surface; h 1,w h is the theoretical wall thickness for each machining cycle. i1,w The wall thickness corresponding to each round of machining; δ d For machining error, d f 11 represents the actual cutting depth, M represents a point on the inner surface during machining; 12 represents the tool; 13 represents the initial wheel data for semi-finishing; 14 represents the intermediate wheel data; 15 represents the final finishing wheel data; 16 represents the input layer of the BP neural network; 17 represents the hidden layer of the BP neural network; 18 represents the actual inner surface point data; and 19 represents the compensation tool position point data. Detailed Implementation

[0060] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings and technical solutions.

[0061] An embodiment of this invention is a complex spherical shell thin-walled component with a diameter of 3350 mm, a height of over 850 mm, a wall thickness requirement of 2 mm in the thinnest area, and relatively complex surface features. Figure 1 This is a flowchart of the mechanism-data-driven method for compensating tool deflection deformation in complex thin-walled parts proposed in this invention. The specific implementation steps are as follows:

[0062] The first step is to solve for the actual internal shape of the workpiece based on the on-machine measurement data.

[0063] The machine tool used in the machining is a gantry five-axis machine tool, whose main structure consists of X-axis, Y-axis, Z-axis, A-axis, and C-axis. Considering the actual structure of the thin-walled spherical shell part, to ensure that the sensor and workpiece do not interfere with each other during the measurement process, and to minimize the amount of data in the overlapping area during profile measurement, thus facilitating subsequent coordinate calculation, a circumferential measurement method is proposed to plan the measurement trajectory. The offset between the actual sensor coordinates and the machine tool coordinates is calibrated, and the actual profile of the workpiece is solved as p using homogeneous transformation theory. i (x i ,y i ,z i A i C i ), (i≤15823769) represents the number of profile sampling points. Based on the actual profile, an electromagnetic ultrasonic thickness measurement trajectory is planned, and workpiece wall thickness information q is collected. j (x j ,y j ,z j A j C j ,d j (j≤256378) represents the number of wall thickness sampling points. Using the neighborhood search algorithm of the PCL point cloud library, the wall thickness information is matched with the profile information to obtain the wall thickness value corresponding to each point of the actual profile, denoted as p. i (x i ,y i ,z i A i C i ,d i ).

[0064] A PCA-based point cloud normal vector estimation method within a neighborhood radius is proposed, which estimates the plane using nearest neighbor points and minimizes the objective function to make p i The dot product of the vector formed by its nearest neighbors and the normal vector is zero.

[0065]

[0066] Where r is the number of points in the neighborhood, and c is the center point of the neighborhood. The normal vector is obtained by solving for the eigenvector of the minimum eigenvalue of the covariance matrix. The solution.

[0067] p i The point is offset inward along the normal vector to the corresponding thickness d i By measuring the distance, the point cloud data of the actual internal surface can be obtained. i (x i ,y i ,z i A i C i ,d i ):

[0068]

[0069] Where x′, y′, z′ are the three-dimensional coordinates of the actual inner surface.

[0070] The second step is to establish a model of the tool deformation mechanism and solve for the compensation compliance coefficient.

[0071] The wall thickness deviation during machining is mainly caused by the deflection of the tool due to the coupling effect of the tool-workpiece system, which causes tool deformation. This error is denoted as δ. d If the process parameters such as feed rate and spindle speed remain constant during machining, then δ d It can be represented as:

[0072] δ d =k′d f (3)

[0073] Where k′ is the compensation compliance coefficient, d f This represents the actual cutting depth.

[0074] According to the calculation theory of thin-walled shells, the formula for calculating the radial deflection deformation of a thin-walled shell micro-element is:

[0075]

[0076] Where F is the radial milling force of the micro-element, and h is the remaining wall thickness.

[0077] The milling force F is generally related to the actual depth of cut, spindle speed, and the properties of the material being machined. Its calculation formula is as follows:

[0078] F = 360 * d f (5)

[0079] Substituting equations (5) and (3) into equation (4), the compensation compliance coefficient k′ can be obtained as follows:

[0080]

[0081] The workpiece profile changes after each machining cycle; therefore, the prediction of the compensation compliance coefficient considers the corresponding point M1 on the inner profile. The theoretical wall thickness for each machining cycle is h. 1,w The actual wall thickness for each processing round is h. i1,w The compensation compliance coefficient for each round of processing is k′ 1,w The actual cutting depth in each round of machining is d. f1,w .

[0082] Based on actual cutting data, the compensation compliance coefficient for subsequent machining processes is predicted using polynomial interpolation. The compensation compliance coefficient k′ for the third round is then calculated. 1,3 for:

[0083]

[0084] To ensure wall thickness accuracy, the sum of the compensation and deformation amounts is 0, resulting in the following equation:

[0085] k′ 1,3 ·(h i1,2 -h 1,3 +c 1,3 )-c 1,3 =0 (8)

[0086] The actual compensation amount c can then be obtained. 1,3 The calculation formula is:

[0087]

[0088] The third step is to predict the actual wall thickness compensation amount based on a BP neural network regression model.

[0089] First, the deformation influence factor is determined to be the actual wall thickness h. i1,w Theoretical processing wall thickness h 1,w Given a spindle speed of 6000 r / min and a tool feed per tooth of 0.15 mm, the input dataset can be represented as X = {x} (1) ,x (2) ,…,x (150000)}, x (i) The feature vector representing historical processed data is denoted as: A backpropagation (BP) neural network model consists of an input layer, hidden layers, and an output layer. The final output model can be represented as follows:

[0090]

[0091] Among them, W (1) W (2) ,b (1) ,b (2) These represent the weights and biases between the input layer and the hidden layer, and between the hidden layer and the output layer, respectively. (1) Z (2) A represents the input to the hidden layer and the output layer, respectively. (1) The output of the hidden layer, v is the output of the model, and v(·) is the activation function.

[0092] The non-linear activation function used is the Sigmoid function, which is calculated as follows:

[0093]

[0094] Where 'a' is the input independent variable.

[0095] Finally, the parameters are updated along the direction of fastest descent of the error function using the backpropagation algorithm to establish an accurate solution model. A partial dataset is used as a test set to validate the prediction model. Finally, the current processing data is used as input to predict the compensation amount c′ for the next round of processing. 1,3 .

[0096] The fourth step is to generate compensation tool points based on the mechanism and data-driven wall thickness compensation values.

[0097] The compensation value c calculated based on the second step of the mechanism analysis model. 1,3 and the compensation value c′ predicted by the third step BP neural network regression model. 1,3 Calculate the average of the predicted values ​​for the corresponding points and use it as the final compensation value. The calculation formula is as follows:

[0098]

[0099] Based on the compensation values ​​calculated at each point in the final solution Combining the actual wall thickness value and the target wall thickness value d at each point ti For each point on the actual inner contour, offset outward along the normal direction to obtain the compensated machining tool position point. The formula for solving the tool position point is:

[0100]

[0101] Where, x tool ,y tool ,z tool The coordinates of the compensation tool position are X, Y, Z.

[0102] Finally, based on the position coordinates and normal vector of the compensation tool point, the compensation machining CNC code is generated. For complex thin-walled parts, multiple rounds of thinning machining are performed. In the roughing stage, a large amount of material is removed by milling according to the theoretical toolpath. Starting from the semi-finishing stage, the work of the second to fourth steps is repeated. This can realize the compensation of tool deformation for complex thin-walled parts driven by both mechanism data, achieve precise control of wall thickness, and meet the actual machining requirements.

[0103] The method described in this invention is applicable to various complex thin-walled parts in aerospace applications where high wall thickness accuracy is required, and has been successfully applied in the field with significant results. It solves the problems of low processing efficiency, difficulty in guaranteeing wall thickness accuracy, and low automation in the processing of complex thin-walled parts. The method described in this invention is simple to operate, highly efficient, fully automated, and highly reliable, meeting the requirements for wall thickness accuracy control in the actual processing of complex thin-walled parts.

[0104] The specific implementation examples described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific implementation examples of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for compensating tool deflection deformation during machining of complex thin-walled parts, driven by both mechanistic data and practical principles, characterized in that... The steps are as follows: The first step is to solve for the actual internal shape of the workpiece based on the on-machine measurement data. Taking into account both the machine tool travel and the actual dimensions of the workpiece, and under the premise that the sensor and workpiece do not interfere with each other and the measurement range is not exceeded, an on-machine measurement trajectory is planned. The actual profile information of the workpiece is then acquired through an external communication method. i (x i ,y i ,z i A i C i ), i≤m, where m is the total number of profile sampling points; based on the actual profile, plan the electromagnetic ultrasonic thickness measurement trajectory and collect the workpiece wall thickness information q. j (x j ,y j ,z j A j C j ,d j ), j≤n, where n is the total number of wall thickness sampling points; since the total number of profile sampling points m is much greater than n, the wall thickness information is matched with the profile information using the Kd-tree neighborhood search algorithm, thus obtaining the wall thickness value corresponding to each point of the actual profile, denoted as p. i ′(x i ,y i ,z i A i C i ,d i ); The neighborhood radius is set based on the sampled point cloud density. Within the neighborhood radius, the PCA point cloud normal vector estimation method is used to estimate the plane using nearest neighbor points. By minimizing the objective function, p i The dot product of the vector formed by a point and its nearest neighbors and the normal vector is zero. Where r is the number of points in the neighborhood, and c is the center point of the neighborhood; let S is a 3x3 covariance matrix. The normal vector is obtained by finding the eigenvector with the smallest eigenvalue of the covariance matrix. The solution; p′ i The point is offset inward along the normal vector to the corresponding thickness d i The distance, i.e., obtaining the point cloud data p of the actual internal surface. i "(x i ',y i ',z i ',A i C i ,d i ): Where x′, y′, z′ are the three-dimensional coordinates of the actual inner surface; The second step is to establish a model of the tool deformation mechanism and solve for the compensation compliance coefficient. When the clamping system is stable, the wall thickness deviation during machining is mainly caused by the deflection and tool deformation resulting from the coupling effect of the tool-workpiece system. This error is denoted as δ. d If the feed rate and spindle speed remain constant during the machining process, then δ d Represented as: d d =k′d f (3) Where k′ is the compensation compliance coefficient, d f This represents the actual cutting depth. According to the calculation theory of thin-walled shells, the formula for calculating the radial deflection deformation of a thin-walled micro-element segment is: Where F is the radial milling force of the micro-element, and E, h, μ are the elastic modulus, remaining wall thickness and Poisson's ratio of the thin-walled part, respectively. The milling force F is related to the actual depth of cut, spindle speed, and the properties of the material being machined. Its calculation formula is as follows: F=k*d f *z t *n rpm (5) Where k is the cutting force coefficient, z t n is the feed per tooth. rpm Main spindle speed; Substituting equations (5) and (3) into equation (4), we obtain the compensation compliance coefficient k′ as follows: The workpiece profile changes after each machining cycle; therefore, the prediction of the compensation compliance coefficient considers the corresponding point M1 on the inner profile. The theoretical wall thickness for each machining cycle is h. 1,w w = 1,...,N; the actual wall thickness for each processing round is h. i1,w The compensation compliance coefficient for each round of processing is k′ 1,w The actual cutting depth in each round of machining is d. f1,w ; The compensation compliance coefficient is closely related to the remaining wall thickness of the workpiece. Based on actual cutting data, the compensation compliance coefficient for subsequent machining processes is predicted using polynomial interpolation. Therefore, the compensation compliance coefficient k′ for the (N+1)th round is... 1,N+1 for: Due to the coupling effect between the compensation amount and the cutting feed rate, the machining error δ d1,N+1 With the actual compensation amount c 1,N+1 They are not equal. To ensure wall thickness accuracy, the sum of the actual compensation and deformation is 0, resulting in the following equation: k′ 1,N+1 ·(h i1,N -h 1,N+1 +c 1,N+1 )-c 1,N+1 =0 (8) That is, the actual compensation amount c can be obtained. 1,N+1 The calculation formula is: The third step is to predict the actual wall thickness compensation amount based on a BP neural network regression model. First, the deformation influence factor is determined to be the actual wall thickness h. i1,w Theoretical processing wall thickness h 1,w Spindle speed n rpm Feed per tooth z t The input dataset is then represented as X = {x} (1) ,x (2) ,…,x (l) }, where l is the number of samples in the training dataset, x (i) The feature vector representing historical processed data is denoted as: Secondly, by removing the dimensions and orders of magnitude differences of different input units, the mean squared error of the input dataset is made relatively small, thus improving the convergence speed. The BP neural network regression prediction model consists of an input layer, hidden layers, and an output layer, and the final output model is expressed as: Among them, W (1) W (2) ,b (1) ,b (2) These represent the weights and biases between the input layer and the hidden layer, and between the hidden layer and the output layer, respectively. (1) Z (2) A is the input to the hidden layer and the output layer, respectively. (1) The output of the hidden layer, v() is the output of the model, and v is the non-linear activation function. The non-linear activation function used is the Sigmoid function, which is calculated as follows: Where 'a' is the input independent variable; Finally, the parameters are updated along the direction of fastest descent of the error function using the backpropagation algorithm to establish an accurate solution model. A partial dataset is used as a test set to verify the BP neural network regression prediction model. Finally, the current processing data is used as input to predict the compensation amount c′ for the next round of processing. 1,N+1 ; The fourth step is to generate compensation tool points based on the mechanism and data-driven wall thickness compensation values. The compensation value c calculated based on the second step of the mechanism analysis model. 1,N+1 and the compensation value c′ predicted by the third step BP neural network regression model. 1,N+1 Calculate the average of the predicted values ​​for the corresponding points and use it as the final compensation value. The calculation formula is as follows: Based on the compensation values ​​calculated at each point in the final solution Combining the actual wall thickness value and the target wall thickness value d at each point ti For each point on the actual inner contour, offset outward along the normal direction to obtain the compensated machining tool position point. The formula for solving the tool position point is: Where, x tool ,y tool ,z tool The coordinates of the compensation tool point are X, Y, Z. Finally, based on the position coordinates and normal vector of the compensation tool point, the compensation machining CNC code is generated. For complex thin-walled parts, multiple rounds of thinning machining are performed. In the roughing stage, a large amount of material is removed by milling according to the theoretical toolpath. From the semi-finishing stage, the work of the second to the fourth steps is repeated. That is, the compensation of tool deformation of complex thin-walled parts driven by both mechanism data is realized, and the wall thickness is accurately controlled to meet the actual machining requirements.

Images