A method for predicting milling forces of an additive manufactured part considering anisotropy

Abstract

This invention proposes a method for predicting milling forces in additively manufactured parts that considers anisotropy, relating to the field of computer-aided design technology. The method includes: designing two sets of micro-milling experiments, with the cutting tools parallel and perpendicular to the stacking direction of the additively manufactured parts, respectively. Each set of micro-milling experiments includes three experiments, with the feed direction adjusted to 0°, 45°, and 90° from the scanning and stacking directions, respectively. The instantaneous milling force magnitude is measured at different feed directions. Based on the measured milling force waveform amplitude, the milling force coefficient is identified. The instantaneous cutting direction angle of the tool element corresponding to the instantaneous milling force coefficient at the current moment is calculated based on geometric mapping relationships. The milling force coefficient is predicted using Gaussian process regression for small sample data. The predicted milling force coefficient is then substituted into the micro-element milling force model to predict the milling force considering anisotropy, thus meeting the requirements of the highly anisotropic characteristics of micro-milling in actual machining of additively manufactured parts.

Description

Technical Field

[0001] This invention relates to the field of computer-aided design technology, and in particular to a method for predicting milling forces in additive manufacturing parts that takes anisotropy into account. Background Technology

[0002] Additive manufacturing (AM), commonly known as 3D printing, is a technology that directly generates objects of any shape by layering materials based on computer graphics data. 3D printing technology is widely used in the forming of various complex parts due to its extremely high degree of design freedom. However, parts obtained solely through 3D printing often have poor surface quality, typically requiring micro-milling to improve surface quality and ensure the parts meet manufacturing requirements.

[0003] When predicting milling forces in additively manufactured parts, two common methods are theoretical modeling and finite element simulation. Existing theoretical modeling methods for predicting milling forces are all for workpieces obtained by macroscopic milling with millimeter-level tools, which are isotropic. However, for additively manufactured parts, according to previous research, the internal structure of additively manufactured parts often exists in the form of columnar grains, and these columnar grains often grow along the stacking direction. When the milling cutter direction is at a certain angle to the columnar grains, there are differences in milling forces and surface quality during the forming process. Existing methods for predicting milling forces in additively manufactured parts do not consider anisotropy, and their prediction results have low accuracy and reliability. Summary of the Invention

[0004] In view of this, the present invention proposes a method for predicting milling force of additively manufactured parts that considers anisotropy, in order to solve the technical problem in the prior art of predicting milling force of additively manufactured parts mentioned above, which does not consider anisotropy and has low accuracy and reliability of prediction results.

[0005] The technical solution of this invention is implemented as follows: This invention proposes a method for predicting milling forces in additively manufactured parts that considers anisotropy, comprising: Two sets of micro-milling experiments were designed, with the cutting tools parallel and perpendicular to the stacking direction of the additively manufactured parts, respectively. Each set of micro-milling experiments included three experiments, with the feed direction adjusted to 0°, 45° and 90° to the scanning direction and the stacking direction, respectively. The milling force was measured at different feed directions. Based on the measured amplitude of the milling force waveform, identify the milling force coefficient; and solve for the instantaneous cutting direction angle of the tool edge micro-element corresponding to the instantaneous milling force coefficient at the current moment based on the geometric mapping relationship. Gaussian process regression was used to perform regression analysis on the milling force coefficients of the two milling cutter orientations for different feed directions, and the predicted milling force coefficients for different feed directions considering anisotropy were obtained. The predicted milling force coefficients for different feed directions are substituted into the micro-element milling force model to predict the milling force.

[0006] In some optional implementations, preferably, identifying the milling force coefficient based on the measured milling force waveform amplitude includes: The cutting edge is divided into multiple discrete infinitesimal elements along the axial direction. The radial, tangential, and axial cutting force coefficients K of each infinitesimal element are determined based on the angle θ between the tool's feed direction and the tool's rotation τ. q (τ), with an axial position of z and a radial position angle of φ j The undeformed chip thickness h(φ) of the blade element at (τ,z) is... j Given the undeformed cutting width db(z) of the tool element at position z (τ,z) and axial position z, calculate the radial, tangential, and axial cutting forces dF of the tool element in the tool element coordinate system. q (φ j (τ,z)) yields the micro-element milling force prediction model; The infinitesimal cutting force is transformed to the tool coordinate system using the transformation matrix T from the tool edge coordinate system. The discrete infinitesimal cutting forces along the Z-axis in the tool coordinate system are then integrated and summed to obtain the total radial, tangential, and axial cutting forces F. q (τ); Based on the radial, tangential, and axial cutting forces dF of the infinitesimal cutting edge element in the coordinate system of the cutting edge element. q (φ j (τ,z) and the total radial, tangential and axial cutting forces F q (τ), and by inverse solution, we obtain the radial cutting force coefficient K at different tool rotation times τ under the current milling angle. r (τ), Tangential cutting force coefficient K t (τ) and axial cutting force coefficient K a (τ).

[0007] In some alternative implementations, preferably, when the undeformed chip thickness is defined in the direction perpendicular to the tool axis vector, the undeformed cutting width db(z) of the tool element at axial position z is equal to the axial discrete element height dz of the tool, based on the radial position angle φ. j (τ,z) and feed per tooth f t Calculate the undeformed chip thickness h (φ) of the blade element. j (τ,z)).

[0008] In some optional embodiments, preferably, the transformation matrix T from the cutting edge coordinate system to the tool coordinate system is derived from the axis tilt angle k(z) and radial position angle φ of the tool element with axial position z. j (τ,z) is calculated.

[0009] In some optional embodiments, preferably, the total radial, tangential, and axial cutting forces F are obtained by integrating and summing the discrete infinitesimal cutting forces along the Z-axis in the tool coordinate system. q (τ), including: Based on the lower boundary z1 and upper boundary z2 representing the cutting edge participating in the cutting, and the total number of cutting teeth N, the discrete infinitesimal cutting force along the Z-axis in the tool coordinate system is integrated and summed to calculate Fq(τ).

[0010] In some optional implementations, preferably, the step of substituting the predicted milling force coefficients for different feed directions into the micro-element milling force model to predict the milling force includes: The predicted instantaneous milling force coefficient K for the two milling cutter orientations q (ψ) and K q Substituting '(ψ') into the infinitesimal milling force prediction model, we obtain the radial, tangential, and axial cutting forces dF in the infinitesimal coordinate system for two milling cutter orientations. q (φ j (τ,z)) and dF q '(φ j (τ',z')); The infinitesimal cutting force is transformed to the tool coordinate system using the transformation matrix T from the tool edge coordinate system. The discrete infinitesimal cutting forces along the Z-axis in the tool coordinate system are then integrated and summed to obtain the total radial, tangential, and axial cutting forces F for both milling cutter orientations. q (τ) and F q '(τ).

[0011] In some alternative implementations, preferably, the radial, tangential, and axial cutting force dF of the cutting edge element in the tool edge element coordinate system is used. q (φ j (τ,z) and the total radial, tangential and axial cutting forces F q (τ), and by inverse solution, we obtain the radial cutting force coefficient K at different tool rotation times τ under the current milling angle. r (τ), Tangential cutting force coefficient K t (τ) and axial cutting force coefficient K a (τ), including: Based on the feed per tooth f t The axial discrete element height dz of the tool, the transformation matrix T from the tool edge coordinate system to the tool coordinate system, and the radial position angle φ. j (τ,z), the number M of the infinitesimal elements involved in the cutting edge, and the cutting force F in the x-direction of the j-th tooth at different tool rotation times τ. x，j (τ), cutting force F in the y direction y，j (τ) and cutting force F in the z directionz，j (τ), calculate the radial cutting force coefficient K at different tool rotation times τ under the current milling angle. r (τ), Tangential cutting force coefficient K t (τ) and axial cutting force coefficient K a (τ).

[0012] In some optional implementations, preferably, the step of solving the instantaneous cutting direction angle of the tool edge micro-element corresponding to the instantaneous milling force coefficient at the current moment based on the geometric mapping relationship includes: Based on the radial position angle φ of the blade at time τ j Given (τ,z) and the angle θ between the tool feed direction and the tool tip direction, calculate the instantaneous cutting direction angle ψ of the tool edge element.

[0013] In some optional implementations, preferably, the step of performing regression analysis on the milling force coefficients for different feed directions of the two milling cutter orientations using Gaussian process regression to obtain predicted milling force coefficients for different feed directions considering anisotropy includes: Assuming the objective function follows a Gaussian process prior, for given training data (ψ, K) q The observed value K with noise ε is calculated based on a Gaussian regression model that takes noise into account. q ; Based on the posterior predicted mean μ * and posterior predicted covariance ∑(ψ) * Calculate the ψ of the new input. * The posterior predicted distribution.

[0014] In some alternative implementations, preferably, the posterior prediction covariance ∑(ψ) * The variance is calculated using a covariance function, which employs a periodic kernel function. This periodic kernel function is determined by a periodic parameter p and a length scale. l Calculate with two input points x and x'.

[0015] In some alternative implementations, preferably, the parameters of the periodic kernel function are automatically optimized using maximum likelihood estimation.

[0016] The method for predicting milling forces in additively manufactured parts that takes anisotropy into account in this invention has the following advantages over the prior art: (1) By identifying the milling force coefficients of different milling cutters and additive manufacturing parts in the stacking direction, the milling force coefficients under small sample data are predicted by Gaussian process regression. The predicted milling force coefficients are then substituted into the micro-element milling force model to predict the milling force considering anisotropy, so as to meet the requirements of the anisotropic characteristics of the micro-milling height of additive manufacturing parts in actual processing. (2) By dividing the cutting edge into multiple discrete infinitesimal elements along the axial direction, the radial, tangential, and axial cutting forces dF of the cutting edge infinitesimal elements in the coordinate system of the cutting edge infinitesimal elements are calculated. q (φ j (τ,z)) is used to obtain the micro-element milling force prediction model; the micro-element cutting force is transformed to the tool coordinate system according to the transformation matrix T from the tool coordinate system to the tool coordinate system, and the discrete micro-element cutting force along the Z-axis in the tool coordinate system is integrated and summed to obtain the total radial, tangential and axial cutting forces F. q (τ); the inverse solution yields the radial cutting force coefficient K at different tool rotation times τ under the current milling angle. r (τ), Tangential cutting force coefficient K t (τ) and axial cutting force coefficient K a (τ); (3) By assuming that the objective function follows a Gaussian process prior, for the given training data (ψ, K) q The observed value K with noise ε is calculated based on a Gaussian regression model that takes noise into account. q Based on the posterior predicted mean μ * and posterior predicted covariance ∑(ψ) * Calculate the ψ of the new input. * The posterior prediction distribution is used to obtain the predicted milling force coefficients for different feed directions considering anisotropy. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a flowchart illustrating the method for predicting milling forces in additive manufacturing parts that considers anisotropy, as described in an embodiment of the present invention. Figure 2 This is a schematic diagram showing the parameter settings for two sets of micro-milling experiments in an embodiment of the present invention; Figure 3 This is a schematic diagram of the instantaneous cutting direction angle and the feed direction angle of the blade element in an embodiment of the present invention; Figure 4 This is a schematic diagram illustrating the solution of the instantaneous cutting direction angle and the feed direction angle of the blade element in an embodiment of the present invention. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0020] In the description of the embodiments of the present invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "connected" and "linked" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium. Those skilled in the art can understand the specific meaning of the above terms in the embodiments of the present invention based on the specific circumstances.

[0021] In the description of the embodiments of the present invention, it should be noted that the terms "center", "longitudinal", "lateral", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", and "outer" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing the embodiments of the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the embodiments of the present invention.

[0022] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0023] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0024] The following disclosure provides numerous different embodiments or examples for implementing various structures of the invention. To simplify the disclosure, specific examples of components and arrangements are described below. These are merely examples and are not intended to limit the invention. Furthermore, reference numerals and / or letters may be repeated in different examples. Such repetition is for simplification and clarity and does not in itself indicate a relationship between the various embodiments and / or arrangements discussed. Additionally, examples of various specific processes and materials are provided in this invention; however, those skilled in the art will recognize the applicability of other processes and / or the use of other materials.

[0025] The technical solution will now be explained in detail: Reference Figures 1-4 As shown in the embodiment of the present invention, a method for predicting milling forces in additively manufactured parts considering anisotropy is proposed, including: Step S1: Design two sets of micro-milling experiments, with the cutting tools parallel and perpendicular to the stacking direction of the additive manufacturing part, respectively. Each set of micro-milling experiments includes three experiments. The feed direction of the three experiments is adjusted to be 0°, 45° and 90° with the scanning direction and the stacking direction, respectively. The milling force of different feed directions is measured.

[0026] Step S2: Identify the milling force coefficient based on the measured amplitude of the milling force waveform; solve for the instantaneous cutting direction angle of the tool edge micro-element corresponding to the instantaneous milling force coefficient at the current moment based on the geometric mapping relationship; Step S2 specifically includes: Step S21: Divide the cutting edge into multiple discrete micro-elements along the axial direction, and determine the instantaneous radial, tangential, and axial cutting force coefficients K of different tool micro-elements under the included angle θ of the tool infeed direction. q (τ), with an axial position of z and a radial position angle of φ j The undeformed chip thickness h(φ) of the blade element at (τ,z) is... j Given the undeformed cutting width db(z) of the tool element at position z (τ,z) and axial position z, calculate the radial, tangential, and axial cutting forces dF of the tool element in the tool element coordinate system. q (φ j (τ,z)) yields the micro-element milling force prediction model; the radial, tangential, and axial cutting forces dF of the micro-element cutting edge in the micro-element coordinate system are obtained; q (φ j (τ,z) can be represented as: (1); In equation (1), dF q (φ j (τ,z) represents the radial, tangential, and axial cutting forces of the tool edge element in the tool edge element coordinate system; K q(τ) represents the angle θ between the tool's feed direction and the radial, tangential, and axial cutting force coefficients of the tool's infinitesimal element under τ-degree rotation; q is one of r, t, and a, representing the radial, tangential, and axial directions, respectively; h(φ) j (τ,z) represents the axial position z and the radial position angle φ. j The undeformed chip thickness of the cutting edge element at (τ,z) is the undeformed cutting width of the cutting edge element at the axial position z. The radial position angle φ in equation (1) j (τ,z) is calculated using the following formula: (2); In equation (2), n is the spindle speed, τ is the tool rotation time, j is the tooth number, N is the total number of teeth, z is the axial position of the tool element, β is the tool helix angle, and R is the tool radius. When the thickness of the undeformed chip is defined in the direction perpendicular to the tool axis vector: (3); In equation (3), dz is the axial discrete element height of the tool; (4); In equation (4), f t This refers to the feed per tooth. Therefore, by combining equations (1), (3), and (4), the radial, tangential, and axial cutting forces of the cutting edge element in the tool edge coordinate system can be expressed as: (5); Step S22: Transform the infinitesimal cutting force into the tool coordinate system using the transformation matrix T from the tool element coordinate system. Then, integrate and sum the discrete infinitesimal cutting forces along the Z-axis in the tool coordinate system to obtain the total radial, tangential, and axial cutting forces F. q (τ); Total radial, tangential, and axial cutting forces F q The formula for calculating (τ) is as follows: (6); In equation (6), T is the transformation matrix from the tool coordinate system to the cutting tool coordinate system, z1 and z2 represent the lower and upper boundaries of the cutting edge participating in the cutting, respectively, and N is the total number of cutting teeth. In equation (6), the transformation matrix T from the cutting edge coordinate system to the tool coordinate system is derived from the axis tilt angle k(z) and radial position angle φ of the tool element with axial position z. j (τ,z) is calculated to yield: (7); In equation (7), k(z) is the axial tilt angle of the tool element with axial position z; Step S23: Based on the radial, tangential, and axial cutting forces dF of the cutting edge micro-element in the tool edge micro-element coordinate system. q (φ j (τ,z) and the total radial, tangential and axial cutting forces F q (τ), and by inverse solution, we obtain the radial cutting force coefficient K at different tool rotation times τ under the current milling angle. r (τ), Tangential cutting force coefficient K t (τ) and axial cutting force coefficient K a (τ). Substituting the radial, tangential, and axial cutting forces of the cutting edge micro-element in the coordinate system of the cutting edge micro-element obtained in step S21 into the three-directional cutting force equation (7) obtained after integration and summation in step S22, we get K. r (τ), K t (τ) and K a The inverse solution formula for (τ): (8); In equation (8), M is the number of infinitesimal elements participating in the cutting edge, and F x，j (τ), F y，j (τ) and F z，j (τ) represents the cutting force in the x direction, y direction, and z direction of the j-th tooth at different tool rotation times τ; Step S24: Based on the radial position angle φ of the blade element at time τ j Given (τ, z) and the angle θ between the tool feed direction and the tool edge, solve for the instantaneous cutting direction angle ψ of the tool edge element. The calculation formula is as follows: (9); In equation (9), mod represents the remainder function; The cutting edge micro-element is located at the center of the axial position, specifically corresponding to the instantaneous cutting direction angle ψ at the axial position z=(z1+z2) / 2. The milling force coefficient K is then applied to the instantaneous cutting direction angle ψ corresponding to the cutting edge micro-element in the three experiments. q (τ) Calculate the average value, eliminate measurement and experimental errors, and obtain the milling force coefficient K of the instantaneous cutting direction angle of the micro-element of the cutting edge under the full angle. q (ψ).

[0027] Step S3: Use Gaussian process regression to perform regression analysis on the milling force coefficients of the two milling cutter orientations for different feed directions, and obtain the predicted milling force coefficients for different feed directions considering anisotropy; Step S3 specifically includes: Step S31: Assume the objective function follows a Gaussian process prior: (10); In equation (10), m(x) is the mean function and k(x,x') is the covariance function; For given training data (ψ, K) q The observed value K with noise ε is calculated based on a Gaussian regression model that takes noise into account. q The specific formula is as follows: (11); In equation (11), ψ is the input, and K q For the observed value with noise ε, σ n 2 To observe the noise variance, I is the identity matrix; Step S32: Based on the posterior predicted mean μ * and posterior predicted covariance ∑(ψ) * Calculate the ψ of the new input. * The posterior predicted distribution; the specific calculation formula is as follows: (12); In equation (12), f * For the test input point ψ * The latent function value at point K; ψ is the input set of the training data; K is the kernel matrix (covariance matrix) of the training data, calculated by the kernel function k(*,*); ψ * For new input; μ * Let ∑(ψ) be the posterior predicted mean. * ) represents the posterior predictive covariance; The posterior prediction mean μ in equation (12) * Calculated using the following formula: (13); The posterior predictive covariance ∑(ψ) in equation (12) * Calculated using the following formula: (14); In equation (14), K(*,*) is the covariance matrix, which satisfies: (15); (16); (17); In equation (17), K(ψ) * ,ψ * The i-th row and j-th column of ) is k(ψ) *i ,ψ *j ); (18); In equation (18), the i-th row and j-th column of K(ψ,ψ) is k(ψ). i ,ψ j ); Step S33: Posterior predicted covariance ∑(ψ) * The variance is calculated using a covariance function, which employs a periodic kernel function. This periodic kernel function is determined by a periodic parameter p and a length scale. l Calculate using two input points x and x'; the calculation formula is as follows: (19); In equation (19), p is a periodic parameter; l The length scale controls the smoothness of the function; x and x' are two input points, respectively. Step S34: Automatically optimize kernel function parameters using maximum likelihood estimation: (20).

[0028] Step S4: Substitute the predicted milling force coefficients for different feed directions into the micro-element milling force model to predict the milling force. Step S4 specifically includes: Step S41: Calculate the predicted instantaneous milling force coefficient K for the two milling cutter orientations. q (ψ) and K q Substituting '(ψ') into the infinitesimal milling force prediction model, we obtain the radial, tangential, and axial cutting forces dF in the infinitesimal coordinate system for two milling cutter orientations. q (φ j (τ,z)) and dF q '(φ j (τ',z')); The calculation formula is as follows: (twenty one); In equation (21), dF q (φ j (τ,z)) and dF q '(φ j (τ', z')) represent the magnitudes of the three-dimensional milling forces of the infinitesimal element when the tool and the stacking direction are parallel and perpendicular to the direction of accumulation, respectively, and K q (ψ) and K q '(ψ') represent the magnitudes of the instantaneous milling force coefficients for two tool orientations: parallel and perpendicular to the tool and the stacking direction, respectively; ψ represents the angle between the instantaneous cutting direction and the scanning direction of the tool element; ψ' represents the angle between the instantaneous cutting direction and the stacking direction of the tool element; h(φ) j (τ,z)) and h(φ) j (τ',z')) represents the instantaneous undeformed cut thickness under two orientations, φ j (τ,z) and φ j(τ',z') represents the radial position angle under the two orientations, τ and τ' represent the tool rotation time under the two tool orientations, z and z' represent the axial position of the cutting edge micro-element under the two orientations, and db(z) and db(z') represent the undeformed cutting width under the two orientations; Step S42: Transform the infinitesimal cutting force into the tool coordinate system using the transformation matrix T from the tool edge coordinate system. Then, integrate and sum the discrete infinitesimal cutting forces along the Z-axis in the tool coordinate system to obtain the total radial, tangential, and axial cutting forces F for both milling cutter orientations. q (τ) and F q The specific calculation formula is as follows: (twenty two); In equation (22), F q (τ) and F q '(τ) represents the magnitude of the three-axis milling force under the two tool orientations, z1 and z1' represent the axial positions of the lower boundary of the cutting edge participating in the cutting under the two tool orientations, respectively; z2 and z2' represent the axial positions of the upper boundary of the cutting edge participating in the cutting under the two tool orientations, respectively.

[0029] The anisotropic milling force prediction method for additively manufactured parts proposed in this invention identifies the milling force coefficients of different milling cutters and additively manufactured parts stacking directions, predicts the milling force coefficients under small sample data through Gaussian process regression, and substitutes the predicted milling force coefficients into the micro-element milling force model to achieve the prediction of milling forces considering anisotropy, so as to meet the requirements of the anisotropic characteristics of micro-milling height of additively manufactured parts in actual processing.

[0030] The above description is only a preferred embodiment of the present invention and is 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 predicting milling forces in additively manufactured parts considering anisotropy, characterized in that, include: Two sets of micro-milling experiments were designed, with the cutting tools parallel and perpendicular to the stacking direction of the additively manufactured parts, respectively. Each set of micro-milling experiments included three experiments, with the feed direction adjusted to 0°, 45° and 90° to the scanning direction and the stacking direction, respectively. The milling force was measured at different times. Based on the measured amplitude of the milling force waveform, identify the milling force coefficient; and solve for the instantaneous cutting direction angle of the tool edge micro-element corresponding to the instantaneous milling force coefficient at the current moment based on the geometric mapping relationship. Gaussian process regression was used to perform regression analysis on the milling force coefficients of the two milling cutter orientations for different feed directions, and the predicted milling force coefficients for different feed directions considering anisotropy were obtained. The predicted milling force coefficients for different feed directions are substituted into the micro-element milling force model to predict the milling force.

2. The method for predicting milling forces in additive manufacturing parts considering anisotropy as described in claim 1, characterized in that, The step of identifying the milling force coefficient based on the measured milling force waveform amplitude includes: The cutting edge is divided into multiple discrete infinitesimal elements along the axial direction. The radial, tangential, and axial cutting force coefficients K of each infinitesimal element are determined based on the angle θ between the tool infeed direction and the tool rotation τ. q (τ), with an axial position of z and a radial position angle of φ j The undeformed chip thickness h(φ) of the blade element at (τ,z) is... j Given the undeformed cutting width db(z) of the tool element at position z (τ,z) and axial position z, calculate the radial, tangential, and axial cutting forces dF of the tool element in the tool element coordinate system. q (φ j (τ,z)) yields the micro-element milling force prediction model; The infinitesimal cutting force is transformed to the tool coordinate system using the transformation matrix T from the tool edge coordinate system. The discrete infinitesimal cutting forces along the Z-axis in the tool coordinate system are then integrated and summed to obtain the total radial, tangential, and axial cutting forces F. q (τ); Based on the radial, tangential, and axial cutting forces dF of the infinitesimal cutting edge element in the coordinate system of the cutting edge element. q (φ j (τ,z) and the total radial, tangential and axial cutting forces F q (τ), and by inverse solution, we obtain the radial cutting force coefficient K at different tool rotation times τ under the current milling angle. r (τ), Tangential cutting force coefficient K t (τ) and axial cutting force coefficient K a (τ).

3. The method for predicting milling forces in additive manufacturing parts considering anisotropy as described in claim 2, characterized in that, When the undeformed chip thickness is defined in the direction perpendicular to the tool axis vector, the undeformed cutting width db(z) of the tool element at the axial position z is equal to the axial discrete element height dz of the tool, according to the radial position angle φ. j (τ,z) and feed per tooth f t Calculate the undeformed chip thickness h (φ) of the blade element. j (τ,z)).

4. The method for predicting milling forces in additive manufacturing parts considering anisotropy as described in claim 2, characterized in that, The transformation matrix T from the blade element coordinate system to the tool coordinate system is obtained through the axis tilt angle k(z) and radial position angle φ of the tool element with axial position z. j (τ,z) is calculated.

5. The method for predicting milling forces in additive manufacturing parts considering anisotropy as described in claim 2, characterized in that, The total radial, tangential, and axial cutting forces F are obtained by integrating and summing the discrete infinitesimal cutting forces along the Z-axis in the tool coordinate system. q (τ), including: Based on the lower boundary z1 and upper boundary z2 representing the cutting edge participating in the cutting, and the total number of cutting teeth N, the discrete infinitesimal cutting force along the Z-axis in the tool coordinate system is integrated and summed to calculate Fq(τ).

6. The method for predicting milling forces in additive manufacturing parts considering anisotropy as described in claim 2, characterized in that, The step of substituting the predicted milling force coefficients for different feed directions into the micro-element milling force model to predict the milling force includes: The predicted instantaneous milling force coefficient K for the two milling cutter orientations q (ψ) and K q Substituting '(ψ') into the infinitesimal milling force prediction model, we obtain the radial, tangential, and axial cutting forces dF in the infinitesimal coordinate system for two milling cutter orientations. q (φ j (τ,z)) and dF q '(φ j (τ',z')); The infinitesimal cutting force is transformed to the tool coordinate system using the transformation matrix T from the tool edge coordinate system. The discrete infinitesimal cutting forces along the Z-axis in the tool coordinate system are then integrated and summed to obtain the total radial, tangential, and axial cutting forces F for both milling cutter orientations. q (τ) and F q '(τ).

7. The method for predicting milling forces in additive manufacturing parts considering anisotropy as described in claim 2, characterized in that, The radial, tangential, and axial cutting forces dF of the cutting edge element in the tool edge infinitesimal coordinate system are described. q (φ j (τ,z) and the total radial, tangential and axial cutting forces F q (τ), and by inverse solution, we obtain the radial cutting force coefficient K at different tool rotation times τ under the current milling angle. r (τ), Tangential cutting force coefficient K t (τ) and axial cutting force coefficient K a (τ), including: Based on feed per tooth f t The axial discrete element height dz of the tool, the transformation matrix T from the tool edge coordinate system to the tool coordinate system, and the radial position angle φ. j (τ,z), the number M of the infinitesimal elements involved in the cutting edge, and the cutting force F in the x-direction of the j-th tooth at different tool rotation times τ. x，j (τ), cutting force F in the y direction y，j (τ) and cutting force F in the z direction z，j (τ), calculate the radial cutting force coefficient K at different tool rotation times τ under the current milling angle. r (τ), Tangential cutting force coefficient K t (τ) and axial cutting force coefficient K a (τ).

8. The method for predicting milling forces in additive manufacturing parts considering anisotropy as described in claim 1, characterized in that, The step of solving the instantaneous cutting direction angle of the tool edge micro-element corresponding to the instantaneous milling force coefficient at the current moment based on the geometric mapping relationship includes: Based on the radial position angle φ of the blade at time τ j Given (τ,z) and the angle θ between the tool feed direction and the tool tip direction, calculate the instantaneous cutting direction angle ψ of the tool edge element.

9. The method for predicting milling forces in additive manufacturing parts considering anisotropy as described in claim 1, characterized in that, The method employs Gaussian process regression to perform regression analysis on the milling force coefficients for different feed directions of the two milling cutter orientations, respectively, to obtain predicted milling force coefficients for different feed directions considering anisotropy, including: Assuming the objective function follows a Gaussian process prior, for given training data (ψ, K) q The observed value K with noise ε is calculated based on a Gaussian regression model that takes noise into account. q ; Based on the posterior predicted mean μ * and posterior predictive covariance ∑(ψ * Calculate the ψ of the new input. * The posterior predicted distribution.

10. The method for predicting milling forces in additive manufacturing parts considering anisotropy as described in claim 9, characterized in that, Posterior predictive covariance ∑(ψ) * The variance is calculated using a covariance function, which employs a periodic kernel function. This periodic kernel function is determined by a periodic parameter p and a length scale. l The periodic kernel function is calculated using two input points x and x'; the parameters of the periodic kernel function are automatically optimized through maximum likelihood estimation.

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