A method for online prediction of milling deformation error

Abstract

In order to solve the problems of increasing production time and cost caused by the method of stopping to detect the machining deformation error, and the machining deformation error cannot be found in time, and the accuracy of the machining deformation error obtained by offline prediction is low, the application provides a kind of milling machining deformation error online prediction method. First of all, the CAGD model of the workpiece and the tool is dispersed based on the method of isogeometric analysis, and the stiffness matrix of the discrete unit is solved according to the material constitutive relation, and then the global stiffness field of the discrete model of the workpiece and the tool is established. Then the cutting force signal is collected in real time during the milling process, and the cutting force signal is mapped to the spatial domain through the interaction with the machine tool, and the actual cutting force distribution related to the position in the milling process is obtained. Finally, the actual cutting force at each position is applied to the global stiffness field of the tool and the workpiece respectively, and the deformation prediction value of the tool and the workpiece is obtained, and the machining deformation error prediction result is obtained by adding.

Description

Technical Field

[0001] This invention relates to the field of machining technology, and in particular to an online method for predicting deformation errors in milling processes. Background Technology

[0002] Milling is characterized by high production efficiency, high machining accuracy, and good machining flexibility, and is widely used in the production of precision parts and complex structural components. The geometrical accuracy of the workpiece directly affects its performance and is an important indicator of the quality of milling. However, during the milling process, due to the cutting force, the tool and workpiece will deform, resulting in a discrepancy between the actual cutting depth and the nominal cutting depth, thus producing machining deformation errors.

[0003] Methods to reduce machining deformation errors typically include adjusting process parameters, compensating for the depth of cut, and optimizing clamping schemes. All of these methods require accurate acquisition of the workpiece's machining deformation error. However, to accurately obtain the workpiece's machining deformation error during milling, machining must be stopped first, and then the workpiece's dimensions must be measured using mechanical or optical inspection methods. While this stop-and-inspection method can obtain relatively accurate machining deformation errors, it significantly increases production time and costs. Therefore, in actual production, machine stops are usually only made between certain processes to arrange for workpiece shape inspection. This results in the inability to detect deformation deviations within a process in a timely manner, making it difficult to adjust the process promptly for remediation. Moreover, continuing to process workpieces with severely out-of-tolerance defects would be a significant waste of time and energy.

[0004] To overcome the drawbacks of using stop-and-detection methods to obtain machining deformation errors, those skilled in the art have proposed methods for offline prediction of machining deformation before machining. However, the milling process is complex and easily affected by uncertainties such as environmental fluctuations, inconsistencies in blank materials, and tool wear, resulting in low accuracy for offline prediction of machining deformation errors before machining.

[0005] In summary, there is an urgent need for an accurate and effective online prediction method for machining deformation during milling, which is of great significance for improving machining accuracy and production efficiency and reducing production costs. Summary of the Invention

[0006] To address the increased production time and costs resulting from current methods of detecting machining deformation errors via downtime inspection, the inability to promptly detect deformation deviations within processes, and the low accuracy of offline prediction methods for obtaining machining deformation errors, this invention provides an online prediction method for milling machining deformation errors. This invention overcomes, to some extent, the limitations of offline prediction based on prior knowledge, serving as an effective supplement to inter-process downtime inspection. It can promptly issue alarms and warnings for deviation issues, providing strong support for process optimization.

[0007] Technical approach of the present invention:

[0008] During machining, both the tool and the workpiece undergo elastic deformation under the action of cutting force and clamping force. This causes the actual tool-workpiece meshing state to differ from the theoretical meshing state, resulting in the actual cutting depth and width being less than the nominal values. Workpiece springback after machining is a major source of machining deformation error. Therefore, this invention first analyzes the deformation characteristics of the workpiece and tool under milling force, then designs a method for obtaining the position-related actual cutting force during machining, comprehensively achieving online prediction of machining deformation error.

[0009] Based on the above ideas, in order to predict machining deformation errors, it is first necessary to establish the mapping relationship between the cutting force of the tool and the workpiece and the deformation, that is, the stiffness distribution.

[0010] For workpieces with simple structures or regular shapes, an analytical model of the workpiece and tool stiffness can be established. The stiffness distribution of the workpiece and tool can be calculated using analytical methods. Then, the deformation during the machining process can be calculated in conjunction with the cutting force, thereby obtaining the machining deformation error.

[0011] For workpieces with complex structures or irregular shapes, it is difficult to establish analytical models of the workpiece and tool stiffness. It is necessary to establish discrete models to solve the stiffness distribution of the workpiece and tool, and then combine the cutting force to solve the deformation during the machining process through finite element calculation.

[0012] Traditional methods for establishing discrete models typically involve uniformly seeding discrete elements along the boundaries of the geometric theoretical model and then performing Lagrange interpolation. If the discrete elements are dense, the calculated stiffness distribution is accurate but computationally time-consuming, resulting in poor timeliness. Conversely, if the discrete elements are sparse, the computation speed is fast but the accuracy is poor. Therefore, existing methods for establishing discrete models struggle to balance accuracy and timeliness in predicting machining deformation for complex structures or irregularly shaped workpieces, making accurate online prediction difficult.

[0013] Hughes et al. proposed the concept of Isogeometry Analysis (IGA), which uses spline basis functions as shape functions and replaces Lagrange interpolation with spline order increase and refinement as the basis for analysis and calculation, achieving high-precision analysis based on Computer-Aided Geometric Design (CAGD) models. Therefore, this invention introduces the isogeometry analysis method when calculating the stiffness distribution of workpieces and tools, avoiding tedious and time-consuming mesh generation. It can refine the discrete model while ensuring the geometric invariance of the computational domain through node insertion and order increase, achieving fast and high-precision solutions for workpiece deformation.

[0014] Secondly, after obtaining the stiffness distribution of the workpiece and the tool, it is also necessary to obtain the cutting force during the machining process.

[0015] Milling removes material from a workpiece using a rotating cutting edge. Cutting forces are generated in the tool-workpiece meshing area, causing deformation of both the tool and workpiece. This deformation, in turn, affects the tool-workpiece meshing area. Therefore, the actual tool-workpiece meshing state and the cutting force have a complex coupling relationship, making it difficult to accurately predict the cutting force and machining deformation offline. Furthermore, various physical quantities are easily affected by uncertainties such as environmental fluctuations, inconsistencies in the workpiece material, and tool wear. Therefore, this invention collects cutting force signals during the milling process and predicts machining deformation errors online based on the actual cutting force to overcome the limitations of offline cutting force predictions.

[0016] However, the cutting force signal directly acquired during machining is a time-domain signal, meaning the cutting force varies with time. Further information regarding the position-dependent force on the workpiece and tool is needed. Since interpolation algorithms differ across CNC machine tools and systems and are not readily available, it is difficult to calculate the actual positions of the tool and workpiece at a given moment based on theoretical toolpaths and process parameters, especially for milling complex structures like blades. Therefore, this invention establishes a method for obtaining position-dependent cutting force distribution through interactive communication with the machine tool and sensors.

[0017] Based on the above technical approach, the inventive concept of this invention is as follows:

[0018] First, the CAGD models of the workpiece and tool are discretized based on the isogeometric analysis method. The stiffness matrix of the discrete element is solved according to the material constitutive relation, and then the global stiffness field of the discrete model of the workpiece and tool is established, that is, the position-related stiffness distribution on the workpiece and tool.

[0019] Then, cutting force signals (time domain signals) are acquired in real time during the milling process. By communicating with the machine tool, the acquired cutting force signals are mapped to the spatial domain to obtain the actual position-related cutting force distribution during the milling process.

[0020] Finally, the actual cutting forces at each location are applied to the global stiffness field of the tool and the workpiece respectively, and the predicted deformation values ​​of the tool and the workpiece are obtained by solving. The results are then added together to obtain the predicted machining deformation error.

[0021] The technical solution of this invention is:

[0022] A method for online prediction of deformation error in milling processes, characterized by the following steps:

[0023] Step 1: Based on the isogeometric analysis method, the CAGD theoretical models of the tool and the workpiece are discretized into discrete models composed of multiple connected and continuously boundaryed discrete units;

[0024] Step 2: Solve for the stiffness matrix of each discrete element in the tool discrete model and the workpiece discrete model respectively;

[0025] Step 3: Establish a method for calculating the equivalent cutting force at each control vertex of the tool discrete model and the workpiece discrete model when the tool and workpiece are subjected to loads;

[0026] Step 4: Based on the stiffness matrix of each discrete element obtained in Step 2 and the calculation method of the equivalent cutting force of each control vertex established in Step 3, establish the global stiffness field of the workpiece discrete model and the tool discrete model respectively.

[0027] Step 5: Real-time acquisition of the actual cutting force at each contact point during the actual machining process;

[0028] Step 6: Apply the actual cutting force to the global stiffness field of the workpiece discrete model and the tool discrete model established in step 4 according to the position of the cutting contact point, and obtain the deformation of the workpiece and the tool at each cutting contact point. Add the deformation of the workpiece and the tool at each cutting contact point to obtain the machining deformation error of the workpiece at each cutting contact point.

[0029] Furthermore, the method for obtaining the discrete model in step 1 is as follows:

[0030] Step 1.1: Define the CAGD theoretical model using a body enclosed by multiple interconnected B-spline surfaces;

[0031] Step 1.2: Increase the order of the B-spline surface;

[0032] Step 1.3: Refine the nodes of the upgraded B-spline surface to obtain new control vertices;

[0033] Step 1.4: Represent the new control vertex in homogeneous form to obtain the control vertex inside the curved body;

[0034] Step 1.5: In the vw, uv, and uw parameter domains, based on the node vectors of the control vertex and the body in the vw, uv, and uw parameter domains, and the order of the body in the v, w, and u directions, the interior of the body is discretized into a set of surfaces along the u, v, and w directions, resulting in three sets of surfaces. The intersection of the three sets of surfaces divides the interior of the body into multiple continuous discrete units, which constitute a discrete model.

[0035] Furthermore, in step 1.2, the Proutz method or the Cohen-Litch-Schumark method is used for order promotion.

[0036] Furthermore, in step 1.3, the Oslo algorithm or the Bohm algorithm is used for node refinement.

[0037] Furthermore, in step 2, the stiffness matrix K of each discrete element is solved using the following formula. e :

[0038]

[0039] In the formula, B is the strain matrix of the discrete element, D is the stress matrix of the discrete element, and V... e It is a discrete unit;

[0040]

[0041]

[0042] In the formula, Let E be the basis function, E be the Young's modulus of the workpiece material, and μ be Poisson's ratio.

[0043] Furthermore, the formulas for calculating the equivalent cutting force at each control vertex of the tool discretization model and workpiece discretization model established in step 3 are as follows:

[0044] f e =R T F p

[0045] In the formula, f e R is the equivalent cutting force, R is the basis function matrix of the discrete element, and T is the matrix transpose operator.

[0046] Furthermore, the method for establishing the global stiffness field of the workpiece discrete model in step 4 is as follows:

[0047] For any point p(u,v,w) on the workpiece discrete model, apply a normal virtual element cutting force F(u,v,w), and solve the equivalent cutting force at the control vertex of each discrete element in the workpiece discrete model according to the method established in step 3, and assemble the equivalent force load matrix.

[0048] Based on the structure of the workpiece, cutting tool and other process equipment in actual processing, and considering the actual clamping method, apply the corresponding boundary conditions to the workpiece discrete model.

[0049] The global static equilibrium equations of the workpiece are established based on the principle of minimum potential energy.

[0050] Substituting the load matrix and boundary conditions, and based on the arrangement order of the discrete elements and the stiffness matrix of each discrete element obtained in step 2, the global static equilibrium equation is solved to obtain the virtual deformation Δ(u,v,w) at any point p(u,v,w) on the workpiece discrete model. Then, the stiffness at any point p(u,v,w) on the workpiece discrete model is calculated.

[0051]

[0052] The method for establishing the global stiffness field of the discrete tool model is the same as that for the discrete workpiece model.

[0053] Furthermore, the method for obtaining the actual cutting force at each contact point in real time during the actual machining process in step 5 is as follows: the cutting force at the current moment is obtained through a force sensor and a data acquisition device, the contact position at the current moment is obtained by accessing the machine tool, and finally the mapping relationship between the contact position and the cutting force is obtained. Based on the mapping relationship, the actual cutting force at each contact point during the machining process is obtained.

[0054] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0055] 1. Considering the stress and elastoplastic deformation analysis of workpieces and cutting tools, continuous physical models are difficult to apply to complex thin-walled parts, and the accuracy of finite element discretization models is limited by the mesh generation scale. This invention adopts an isogeometric analysis method, which can simultaneously satisfy geometric calculation and finite element analysis. It uses spline basis functions as shape functions, replacing the Lagrange interpolation used in traditional finite element discretization methods with their order increase and node refinement. Using parameterized curved bodies as elements, it achieves high-precision discretization analysis of the stiffness distribution of workpieces and cutting tools based on the CAGD theoretical model, and has the following advantages:

[0056] 1) Shape functions have good convergence and can achieve high-precision solutions for complex structural parts such as thin shells and freeform surfaces;

[0057] 2) It eliminates the need for cumbersome computational domain mesh generation, providing support for the mutual conversion between CAGD theoretical models and finite element discrete models;

[0058] 3) Model element refinement can be achieved by methods such as node insertion and order increase, while keeping the computational domain geometry unchanged.

[0059] In summary, this invention uses the isogeometric analysis method to discretize the CAGD model, resulting in continuous geometric boundaries of the discrete elements. The discrete model composed of these discrete elements is absolutely accurate and unaffected by the density of the discrete elements. This approach can simultaneously guarantee the calculation accuracy and efficiency of the stiffness distribution of the workpiece and the tool, providing a foundation for online prediction of deformation errors.

[0060] 2. The milling process of complex structural parts involves complex physical mechanisms, with various physical quantities coupled together. Numerous influencing factors and susceptibility to environmental fluctuations make accurate prediction of cutting forces difficult. If actual cutting force signals are used for prediction, the force monitoring signals collected by sensors at the machining site are recorded and stored over time, lacking spatial location information and thus unsuitable for force and deformation analysis of complex workpieces. Furthermore, due to the different and unpredictable feed interpolation algorithms of different machine tools and CNC systems, coupled with the influence of external environmental disturbances, calculating the tool position and machining progress at any given moment based on theoretical toolpaths and machining parameters is infeasible, resulting in significant deviations from actual values. To address this issue, this invention simultaneously reads the machine tool spindle motion information during the milling process to obtain the time-varying pattern of the tool position; it then correlates and retrieves the time-domain cutting force signals collected by sensors to obtain position-related cutting force signal values. This expands the time-dependent process data into spatiotemporally dependent process data, enabling its application in force and deformation analysis of complex workpieces.

[0061] 3. This invention applies the actual cutting force at each contact point during the machining process to the global stiffness field of the established discrete workpiece model and discrete tool model, thereby obtaining the deformation of the workpiece and tool respectively. By summing the deformation of the workpiece and tool, the machining deformation error at any point on the workpiece surface can be obtained, thus realizing online prediction of milling machining deformation error. Attached Figure Description

[0062] Figure 1 This is a flowchart of the method of the present invention.

[0063] Figure 2 This is an example diagram of a B-spline curve and its control vertices.

[0064] Figure 3 This is an example diagram of a B-spline surface and its control vertices.

[0065] Figure 4 This is an example diagram of a B-spline body and its control vertices.

[0066] Figure 5 This is an example diagram of an upgraded B-spline curve.

[0067] Figure 6 It is a CAGD model defined by several B-spline surfaces connected end to end.

[0068] Figure 7 This is an example of the discrete results of a CAGD model obtained through isogeometric analysis.

[0069] Figure 8 It is a measurement chain for cutting force signals during the machining process.

[0070] Figure 9 This is a schematic diagram of a cutting force time-domain signal.

[0071] Figure 10 This is a schematic diagram of the time-domain signal being mapped to the signal spatial distribution.

[0072] Figure 11 This is a schematic diagram illustrating an example of interactive communication with a machine tool.

[0073] Figure 12 This is an example diagram of the stiffness field of a cutting tool.

[0074] Figure 13 This is an example diagram of the stiffness field of a blade.

[0075] Figure 14 This is an example diagram showing the deformation of a cutting tool under cutting force.

[0076] Figure 15 This is an example diagram showing the deformation of a blade under cutting force.

[0077] Figure 16 This is a schematic diagram illustrating the sources of machining deformation errors. Detailed Implementation

[0078] To facilitate understanding of the technical solution of this invention, a brief introduction to rational B-splines is provided first. Rational B-splines, as a fundamental method for mathematical description of shapes, were proposed by Gordon and Riesenfeld and have become an industry standard for shape representation, design, and data exchange when processing geometric information using computers. For example, Figure 2 , Figure 3 and Figure 4 These represent B-spline curves, surfaces, and solids, respectively. The black dots in the figure represent the control vertices of the curves, surfaces, and solids. Based on the Standard for the Exchange of Product Model Data (STEP), the definition of B-spline surfaces and related terminology are provided here as an example.

[0079] Definition 1: Given (m+1)×(n+1) control vertices d i,j Given an array of nodes (i = 0, 1, ..., m; j = 0, 1, ..., n), with parameters u and v and their powers k and l, and a node vector U = [u0, u1, ..., u2], ..., ... m+k+1 ] and V = [v0, v1, ..., v n+l+1 That is, define a k×l B-spline surface with the following parametric equations:

[0080]

[0081] uk ≤u≤u m+1 ,v l ≤v≤v n+1

[0082] Wherein, the B-spline basis function N i,k (u)(i=0,1,…,m) and N j,l (v)(j=0,1,...,n) has multiple equivalent definitions. In modern international standard algorithms, the B-spline basis function is determined by the node vectors U and V according to the DeBoor-Cox recursive formula. The control vertices, the degree of each control vertex, and the node vectors are determined when establishing the CAGD model.

[0083] Definition 2: If there are ω control vertices ξ among all control vertices of a B-spline surface, then the repeatability of the control vertex ξ is called ω.

[0084] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings.

[0085] Reference Figure 1 The online prediction method for milling deformation error provided by the present invention includes the following steps:

[0086] Step 1: Discretize the CAGD theoretical models of both the tool and the workpiece into discrete models composed of multiple connected and continuously bounded discrete units.

[0087] In product model data exchange standards, the CAGD theoretical model of a workpiece and tool is defined by a body surrounded by multiple interconnected boundary surfaces, which are B-spline surfaces. For CAGD theoretical models of complex structures such as aero-engine blades, the distribution of geometric features such as curvature on the boundary surfaces of the CAGD theoretical model is uneven during design. Therefore, the control vertices of the B-spline surfaces constituting the boundary surfaces of the CAGD theoretical model are unevenly distributed. Directly using these surfaces to construct a discrete model would result in excessively large discrete element volumes in regions with sparse control vertices, leading to an overall uneven distribution of discrete elements.

[0088] Therefore, the first step is to increase the order of the B-spline curve to enhance its flexibility; this process is called order increase, and typical methods include the Proutz method and the Cohen-Litch-Schumark method. Next, new control vertices need to be inserted into the existing control vertices of the B-spline surface to increase the number of control vertices; this process is called node refinement, and methods include the Oslo algorithm and the Bohm algorithm. Through order increase and node refinement, the flexibility of shape control can be precisely increased in a specific region. Intuitively, Figure 5 This is an example of an increased order B-spline curve.

[0089] For example, such as Figure 6As shown, a CAGD theoretical model is defined by a body enclosed by 6 interconnected boundary surfaces, all of which are B-spline surfaces. Extending the definition of B-spline surfaces, let these 6 boundary surfaces be S(0,v,w), S(1,v,w), S(u,0,w), S(u,1,w), S(u,v,0) and S(u,v,1), where u, v, and w are the parameters of the parametric equations of the B-spline surfaces.

[0090] Define the maximum order p in the u-direction of the boundary surfaces S(u,0,w), S(u,1,w), S(u,v,0), and S(u,v,1) as the order p of the body in the u-direction, and upgrade the boundary surfaces with orders less than p to order p. At the same time, take the union of the u-direction node vectors of the boundary surfaces S(u,0,w), S(u,1,w), S(u,v,0), and S(u,v,1) as the node vector U in the u-direction of the upgraded body, and the corresponding node repetition is the maximum node repetition among the boundary surfaces S(u,0,w), S(u,1,w), S(u,v,0), and S(u,v,1).

[0091] Define the maximum order q of the boundary surfaces S(0,v,w), S(1,v,w), S(u,v,0), and S(u,v,1) in the v direction as the v-direction order of the body, and upgrade boundary surfaces with orders less than q to order q. At the same time, take the union of the v-direction node vectors of the boundary surfaces S(0,v,w), S(1,v,w), S(u,v,0), and S(u,v,1) as the node vector V of the upgraded body in the v direction, and the corresponding node repetition is the maximum node repetition among the boundary surfaces S(0,v,w), S(1,v,w), S(u,v,0), and S(u,v,1).

[0092] Define the maximum order r of the boundary surfaces S(0,v,w), S(1,v,w), S(u,0,w), and S(u,1,w) in the w direction as the order of the body in the w direction, and upgrade the boundary surfaces with orders less than r to order r. At the same time, take the union of the node vectors in the w direction of the boundary surfaces S(0,v,w), S(1,v,w), S(u,0,w), and S(u,1,w) as the node vector W in the w direction of the upgraded body, and the corresponding node repetition is the maximum node repetition among the boundary surfaces S(0,v,w), S(1,v,w), S(u,0,w), and S(u,1,w).

[0093] The boundary surface after the order upgrade is refined at each node to obtain new control vertices. Let the new control vertices be ξ. 0,j,k ξ 1,j,k ξ i,0,k ξ i,1,k ξ i,j,0 and ξ i,j,1Let i, j, and k represent the positions of the control vertex in the surface control vertex array (i = 0, 1, ..., n; j = 0, 1, ..., m; k = 0, 1, ..., l). Let the repetition degree corresponding to the new control vertex be ω. 0,j,k ω 1,j,k ω i,0,k ω i,1,k ω i,j,0 ω i,j,1 .

[0094] Obtain the parametric equations of the curved body

[0095]

[0096] Representing the new control vertices of the boundary surface obtained after refining the execution nodes in order upgrade form as homogeneous, the control vertices inside the body are:

[0097]

[0098] In the vw parameter domain, for any By a given control vertex Given the node vectors V and W of the curved body in the v and w directions, and the powers q and r of the curved body in the v and w directions, the surface is obtained according to the definition of a B-spline surface. Will Traversing {0,1,…n} yields a set of surfaces {φ0,φ1,…φn} along the u direction inside the curved body. n}

[0099] The same method can be used to obtain the curved surfaces inside the body along the v and w directions. and {ψ0,ψ1,…ψ l}, three sets of surfaces {φ0,φ1,…φ n}、 and {ψ0,ψ1,…ψ l The intersection divides the interior of the curved body into (n+1)×(m+1)×(l+1) mutually continuous discrete units. Each discrete unit is also defined by a curved body surrounded by interconnected boundary surfaces, which are still B-spline surfaces.

[0100] In summary, a CAGD theoretical model defined by several B-spline surfaces is discretized into a discrete model composed of multiple interconnected and continuously bounded discrete units. For example, the discretization result is as follows: Figure 7 As shown.

[0101] Step 2: Solve for the stiffness matrix of each discrete element in the tool discrete model and the workpiece discrete model respectively.

[0102] Establish a three-dimensional linear elastic static equilibrium model of discrete elements, and solve the stiffness matrix of the discrete elements based on the principle of virtual work or the principle of minimum potential energy (the two are equivalent).

[0103] Specifically, discrete unit V e stiffness matrix K e Solve using the following formula:

[0104]

[0105] In the formula, B is the strain matrix of the discrete element, and D is the stress matrix of the discrete element.

[0106] Let the union of the control vertices of the boundary surface of the discrete element be... The strain matrix B can be calculated by the following formula:

[0107]

[0108] In the formula, These are basis functions.

[0109] The stress matrix D can be calculated by the following formula:

[0110]

[0111] In the formula, E is the Young's modulus of the workpiece material; μ is Poisson's ratio; both are inherent properties of the material and need to be obtained based on basic mechanical experiments of the actual processed material.

[0112] Step 3: Establish a solution method for the equivalent cutting force of the control vertex of each discrete unit in the discrete model.

[0113] During the cutting process, the coordinates of the contact position between the tool and the workpiece at a certain moment are (x, y, z), and the tool contact point at that moment is called p = (x, y, z). Since it is necessary to obtain the force vector on the control vertex before solving the discrete model using the finite element method, it is necessary to transfer the cutting force load on the tool contact point to the control vertex. At the same time, the static equivalence principle should be followed during the transfer process.

[0114] The equilibrium differential equation of the discrete element can be expressed as:

[0115] K e U e =F e

[0116] In the formula, K e U is the stiffness matrix of the discrete element; e F is the strain matrix of the discrete element, i.e., the strain matrix B in step 2; e Let D be the stress matrix of the discrete element, i.e., the stress matrix D in step 2.

[0117] When the cutting point is p, the workpiece is subjected to a concentrated force F. p According to the principle of virtual work equivalence, the cutting force load at the original tool contact point p (which can be obtained in step 5) is equal to the virtual work of the cutting force at the control vertex at any virtual displacement, i.e.

[0118]

[0119] In the formula, To control the virtual displacement matrix of the vertices (an intermediate variable that will be eliminated by subsequent equation transformations and substitutions), f represents the virtual displacement at the cutting contact point p of the tool, with the superscript T representing the matrix transpose operator. e To control the equivalent cutting force at the vertex.

[0120] Based on the properties of B-splines

[0121]

[0122] In the formula, R is the basis function matrix of the discrete unit.

[0123] In summary, we obtain the values ​​of each discrete unit V in the discrete model. e A concentrated force F is applied at the cutting point p of the tool. p The equivalent cutting force f at the control vertex e :

[0124] f e =R T F p

[0125] Step 4: Establish the global stiffness fields for the discrete models of the workpiece and the tool, respectively.

[0126] The methods for solving the global stiffness field of the workpiece and the tool are the same. Here, we will take the method for establishing the global stiffness field of the workpiece discrete model as an example. Let the parameters of the parametric equation of the workpiece discrete model be u, v, and w. The set of all possible values ​​of the parameters constitutes the parameter domain.

[0127] For any point p(u,v,w) on the workpiece discrete model, apply a normal virtual element cutting force F(u,v,w). Solve for the equivalent cutting force at the control vertex of each discrete element in the workpiece discrete model using the method established in step 3, and assemble the equivalent load matrix. Based on the structure of the workpiece, tool, and other process equipment in actual machining, and considering the actual clamping method, apply corresponding boundary conditions to the workpiece discrete model. Establish the global static equilibrium equation of the workpiece based on the principle of minimum potential energy. Substitute the load matrix and boundary conditions, and according to the arrangement order of the discrete elements and the stiffness matrix of each discrete element (obtained from step 2), solve the global static equilibrium equation to obtain the virtual deformation Δ(u,v,w) at any point p(u,v,w) on the workpiece discrete model, and then calculate the stiffness at any point p(u,v,w) on the workpiece discrete model.

[0128]

[0129] In summary, this yields the global stiffness field related to the workpiece's position. The method for establishing the global stiffness field of the tool is similar to that for the workpiece.

[0130] For example, such as Figure 12 and 13 As shown.

[0131] Step 5: Real-time acquisition of the actual cutting force at each contact point during the milling process.

[0132] like Figure 8 As shown, a force sensor is connected to a data acquisition unit, which in turn is connected to a computer, allowing for real-time acquisition and storage of force monitoring signals during the milling process. However, the force monitoring signals acquired in this way are time-domain signals, meaning that the acquired signals represent the cutting force-time mapping relationship, i.e., the variation of the cutting force over time. Figure 9 To obtain the distribution pattern of cutting force along the tool's motion trajectory, it is also necessary to obtain the change pattern of the tool's spatial position over time. CNC machine tools equipped with servo motors can obtain the real-time position of the machine spindle by accessing data from the machine's programmable logic controller (PLC). Modern CNC machine tools' CNC systems allow connection to a computer, indirectly obtaining the machine spindle position at any given time through communication with the CNC system. For example, Figure 11 This paper presents a case study of communication and interaction between an industrial control computer and a CNC system. After obtaining the real-time machine tool spindle position, the cutting contact position corresponding to the current machine tool spindle position can be calculated based on the tool's geometric parameters and tool clamping length.

[0133] The cutting force at the current moment is obtained through a force sensor and a data acquisition unit. The cutting contact position at the current moment is obtained by accessing the machine tool. Finally, the mapping relationship between the cutting contact position and the cutting force is obtained, such as... Figure 10 As shown.

[0134] By mapping the contact point to the cutting force, the actual cutting force at each contact point during machining can be obtained.

[0135] Step 6: Predicting machining deformation.

[0136] Establish the global stiffness fields for the workpiece and tool respectively in step 4. and The actual cutting force at each contact point during the machining process The global stiffness fields of the workpiece discrete model and the tool discrete model established in step 4 are applied respectively to obtain the deformations of the workpiece and the tool. and

[0137]

[0138]

[0139] During machining, both the workpiece and the cutting tool will deform under the action of cutting forces, for example, as shown in the example. Figure 14 and 15 As shown. The machining deformation error at any point on the workpiece surface is the vector sum of the deformations of the workpiece and the tool under the cutting force when the tool reaches that position during machining. The principle behind the machining deformation error is as follows. Figure 16 As shown, the machining deformation error of the workpiece at the contact point p(u,v,w) is... for

[0140]

Claims

1. A method for online prediction of deformation error in milling processes, characterized in that, Includes the following steps: Step 1: Based on the isogeometric analysis method, the CAGD theoretical models of the tool and the workpiece are discretized into discrete models composed of multiple connected and continuously boundaryed discrete units; Step 1.1: Define the CAGD theoretical model using a body enclosed by multiple interconnected B-spline surfaces; Step 1.2: Increase the order of the B-spline surface; Step 1.3: Refine the nodes of the upgraded B-spline surface to obtain new control vertices; Step 1.4: Represent the new control vertex in homogeneous form to obtain the control vertex inside the curved body; Step 1.5: In , and In the parameter domain, based on the control vertex and the curved body... , and The node vectors in the parameter domain, and the curves in , , The number of times the order is increased in the direction will move the interior of the curve along... , , Each direction is discretized into a set of surfaces, resulting in three sets of surfaces. The intersection of these three sets of surfaces divides the interior of the body into multiple continuous discrete units, which constitute a discrete model. Step 2: Solve for the stiffness matrix of each discrete element in the tool discrete model and the workpiece discrete model respectively; Step 3: Establish a method for calculating the equivalent cutting force at each control vertex of the tool discrete model and the workpiece discrete model when the tool and workpiece are subjected to loads; Step 4: Based on the stiffness matrix of each discrete element obtained in Step 2 and the calculation method of the equivalent cutting force of each control vertex established in Step 3, establish the global stiffness field of the workpiece discrete model and the tool discrete model respectively. Step 5: Real-time acquisition of the actual cutting force at each contact point during the actual machining process; Step 6: Apply the actual cutting force to the global stiffness field of the workpiece discrete model and the tool discrete model established in step 4 according to the position of the cutting contact point, and obtain the deformation of the workpiece and the tool at each cutting contact point. Add the deformation of the workpiece and the tool at each cutting contact point to obtain the machining deformation error of the workpiece at each cutting contact point.

2. The online prediction method for milling deformation error according to claim 1, characterized in that: In step 1.2, the Proutz method or the Cohen-Litch-Schumark method is used for order promotion.

3. The online prediction method for milling deformation error according to claim 2, characterized in that: In step 1.3, the Oslo algorithm or the Bohm algorithm is used to refine the nodes.

4. The online prediction method for milling deformation error according to any one of claims 1-2, characterized in that: In step 2, the stiffness matrix of each discrete element is solved using the following formula. : In the formula, The strain matrix of the discrete element. The stress matrix of the discrete element. It is a discrete unit; In the formula, As basis functions, The Young's modulus of the workpiece material; It is Poisson's ratio.

5. The online prediction method for milling deformation error according to any one of claims 1-2, characterized in that: The formulas for calculating the equivalent cutting force at each control vertex of the tool discretization model and workpiece discretization model established in step 3 are as follows: In the formula, For equivalent cutting force, Let be the basis function matrix of the discrete unit. This is the matrix transpose operator.

6. The online prediction method for milling deformation error according to any one of claims 1-2, characterized in that: The method for establishing the global stiffness field of the workpiece discrete model in step 4 is as follows: For any point on the discrete model of the workpiece Apply normal virtual element cutting force The equivalent cutting force at the control vertex of each discrete unit in the discrete model of the workpiece is solved according to the method established in step 3, and the equivalent load matrix is ​​assembled. Based on the structure of the workpiece, cutting tool and other process equipment in actual processing, and considering the actual clamping method, apply the corresponding boundary conditions to the workpiece discrete model. The global static equilibrium equations of the workpiece are established based on the principle of minimum potential energy. Substituting the load matrix and boundary conditions, and based on the arrangement order of the discrete elements and the stiffness matrix of each discrete element obtained in step 2, the global static equilibrium equation is solved to obtain the equilibrium equation for any point on the discrete model of the workpiece. Virtual deformation at the location Then, any point on the discrete model of the workpiece can be calculated. Stiffness at the point: ； The method for establishing the global stiffness field of the discrete tool model is the same as that for the discrete workpiece model.

7. The online prediction method for milling deformation error according to any one of claims 1-2, characterized in that: The method for obtaining the actual cutting force at each contact point in real time during the actual machining process in step 5 is as follows: the cutting force at the current moment is obtained through a force sensor and a data acquisition device, the contact position at the current moment is obtained by accessing the machine tool, and finally the mapping relationship between the contact position and the cutting force is obtained. Based on the mapping relationship, the actual cutting force at each contact point during the machining process is obtained.

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