A method for generating toolpaths for high-efficiency, low-acceleration multi-axis machining of complex curved surfaces

Abstract

This invention belongs to the field of CAD / CAM technology for complex curved surfaces, specifically relating to a method for generating toolpaths for high-efficiency, low-acceleration multi-axis machining of complex curved surfaces. The method includes: discretizing the surface to be machined into n feature points using discrete precision based on the normal vector of the surface; constructing an objective function at each discrete feature point to maximize high-efficiency, low-acceleration machining of the surface; then, using the sum of the objective functions corresponding to each discrete feature point as the optimization objective, and the surface machining trajectory, tool axis vector, and workpiece mounting posture as optimization variables, establishing a surface machining optimization mathematical model; solving this optimization mathematical model to obtain the optimal toolpath generation parameters; and finally, generating the machining trajectory of the entire surface based on the optimized toolpath generation parameters. The entire toolpath planning process is programmable, and the planned machining toolpath can achieve high area removal rate machining of complex curved surfaces under low acceleration.

Description

Technical Field

[0001] This invention belongs to the field of CAD / CAM technology for complex curved surfaces, specifically relating to a method for generating toolpaths for high-efficiency, low-acceleration multi-axis machining of complex curved surfaces. Background Technology

[0002] Multi-axis machining of complex curved surfaces has always been a research hotspot internationally, playing a dominant role in the processing of key components in manufacturing fields such as aerospace. Academician Ding Han pointed out that "five-axis CNC machining is an effective means of efficiently machining complex parts in fields such as aviation, aerospace, energy, and defense, and is a technological breakthrough for improving my country's manufacturing level. The National Natural Science Foundation of China, the National Key Basic Research and Development Program, and major science and technology projects all list the basic theories and common technologies of five-axis CNC machining as key research directions." However, due to the curvature variation characteristics of complex curved surfaces and the complexity of five-axis machine tool motion, the five-axis machining process for complex curved surfaces is a very complex process. Machining efficiency, part quality, energy consumption, and machine tool wear are all issues that need to be considered uniformly in CNC machining. Furthermore, how to optimize machining process variables, scientifically evaluate the quality of the machining process, and simultaneously achieve low-cost, high-precision, and high-efficiency machining are fundamental scientific problems that urgently need to be solved in the current field of multi-axis machining.

[0003] The paper "Hu P, Chen L, Tang K. Efficiency-optimal iso-planar tool pathgeneration for five-axis finishing machining of freeform surfaces[J]. Computer-Aided Design, 2017:S0010448516301270." proposes a toolpath optimization method with the machining path width multiplied by the feed rate as the objective. However, this method maximizes the machine tool cutting efficiency by running the acceleration, speed and acceleration of a certain axis of the machine tool under extreme conditions, without considering the machine tool wear caused by the acceleration.

[0004] The paper "Xu J, Zhang D, Sun Y. Kinematics performance-oriented smoothing method to plan tool orientations for 5-axis ball-end CNC machining[J]. International Journal of Mechanical Sciences, 2019, 157-158: 293-303." proposes a toolpath generation method that considers machine tool motion performance, that is, optimizing tool orientation in the machine tool coordinate system with minimizing the acceleration of the rotary axis as the optimization objective. However, this method only considers the acceleration of the machine tool rotary axis and fails to consider the toolpath machining efficiency at the same time, that is, cutting performance such as machining path width is not mentioned.

[0005] The literature “Xu Jinting, Niu Jinbo, Chen Mansen, et al. Research progress on multi-axis CNC machining technology for precision complex curved surface parts [J]. Acta Aeronautica Sinica, 2021, 42(10):24.” and “Sun Y, Jia J, Jinting XU, et al. Path, feedrate and trajectory planning for free-from surface machining: A state-of-the-art review [J]. Chinese Journal of Aeronautics, 2021(13.]” both point out that considering both the motion performance of the machine tool and the cutting performance of the tool in the machine tool coordinate system is an important development direction for tool trajectory planning and attitude optimization of complex curved surfaces.

[0006] In summary, traditional multi-axis machining of complex curved surfaces has the following drawbacks:

[0007] 1) Improving the product of the machining width and feed rate of curved surfaces, i.e., the "machining area removal rate", is an important way to improve the efficiency of curved surface machining and an important development direction of multi-axis machining technology. However, current research mainly focuses on using the machine tool to operate at maximum acceleration to improve the feed "machining area removal rate", while ignoring the machine tool wear, high energy consumption and curved surface machining quality problems caused by high acceleration.

[0008] 2) Few scholars have improved the "machining area removal rate" by optimizing the machining trajectory topology planning, tool posture, workpiece mounting posture, and machine tool and fixture structure to reduce the machine tool acceleration limit. However, this approach has greater potential for improvement in "machining area removal rate" and is more likely to yield a reasonable and ideal five-axis machining method.

[0009] 3) Reducing the acceleration of the machine tool motion axis during the machining process is an important technical means to reduce machine tool wear, reduce energy consumption and improve the machining quality of complex curved surfaces. However, the machining efficiency of curved surfaces is neglected in this process, and the optimization of the "machining area removal rate" of curved surfaces is lacking.

[0010] 4) There are many existing evaluation indicators for complex surface five-axis machining processes, such as high machining area removal rate, low acceleration of machine tool motion axes, and low machining energy consumption. However, these evaluation methods have limitations. They do not balance machining efficiency and machine tool acceleration, and cannot simultaneously meet the objective requirements of high efficiency, high precision, and low cost manufacturing. Therefore, it is necessary to develop scientific quantitative evaluation methods. Summary of the Invention

[0011] (a) Technical problems to be solved

[0012] This invention addresses the above-mentioned problems by proposing a method for generating toolpaths for high-efficiency, low-acceleration multi-axis machining of complex curved surfaces. The aim is to solve the comprehensive technical problems in multi-axis machining of complex curved surfaces, including machine tool wear, energy consumption, machining efficiency, and machining quality.

[0013] (II) Technical Solution

[0014] To achieve the above objectives, this invention provides a method for generating toolpaths for high-efficiency, low-acceleration multi-axis machining of complex curved surfaces, the method comprising the following steps:

[0015] Discretize the surface to be processed based on the surface normal vector to obtain the surface feature points;

[0016] Construct an objective function at each feature point to achieve high-efficiency, low-acceleration surface processing;

[0017] A mathematical model for surface processing optimization is established, taking the sum of the objective functions at each feature point as the optimization objective.

[0018] The mathematical model was solved using a constrained optimization method to obtain the optimal parameters for toolpath generation.

[0019] The machining toolpath for the surface to be machined is generated based on the optimal toolpath generation parameters.

[0020] Furthermore, the steps for constructing the objective function at each feature point to achieve high-efficiency, low-acceleration surface processing include:

[0021] feature point p i Let the origin be point p. i The principal normal vector of the surface is the z-axis, and the tangent vector along the u-axis is the x-axis. Establish a local coordinate system oxyz with the y-axis as the coordinate axis;

[0022] Rotate the xoz plane counterclockwise around the z-axis by an angle denoted as θ.i The rotation plane p-θ is obtained. i Rotation plane p-θ i The intersection line with the given surface S to be processed is denoted as L. i ;

[0023] In L i Above, with step size Δs at p i Take one point before and one point after, and denote them as follows: and

[0024] Based on the requirements of high efficiency and low acceleration in machining toolpaths, at point p i Establish the objective function η for achieving high-efficiency, low-acceleration machining. i .

[0025] Furthermore, at point p i In the step of establishing the objective function to achieve high-efficiency, low-acceleration machining, the objective function η i Represented as s i -c i , where s i c represents the processing area removal rate. i This represents the acceleration of the machine tool.

[0026] Furthermore, where s i This indicates that, given a feed rate λ, for a point p on the surface... i Any machining direction θ, tool rake angle α, and tool sideslip angle β, p i Processing line width d i It is a function of θ, α, and β, that is:

[0027] s i =s i (θ,α,β)=λ*d i (θ,α,β).

[0028] Furthermore, where c i The representative term of machine tool acceleration is defined as follows:

[0029] c i =ω i (m A α iA +m B α iB +m x α ix +m y α iy +m z α iz ),

[0030] Where, ω iThe positive correlation coefficient, m A The A-axis at point p i The corresponding quality weighting coefficient, α iA The A-axis at point p i The corresponding acceleration; m B The B-axis at point p i The corresponding quality weighting coefficient, α iB The B-axis at point p i The corresponding acceleration; m x The x-axis at point p i The corresponding quality weighting coefficient, α ix The x-axis at point p i The corresponding acceleration; m y The y-axis at point p i The corresponding quality weighting coefficient, α iy The y-axis at point p i The corresponding acceleration; m z The z-axis at point p i The corresponding quality weighting coefficient, α iz The z-axis at point p i The corresponding acceleration.

[0031] Furthermore, where c i It is expressed as a function of machining trajectory (θ), tool axis vector (α, β), and workpiece mounting posture (x, y, z, φ(x), φ(y), φ(z)), i.e.:

[0032] c i =c i (θ,α,β,x,y,z,φ(x),φ(y),φ(z)).

[0033] Furthermore, in the step of constructing the mathematical model for surface machining optimization, the optimization variables include the surface machining trajectory, the tool axis vector, and the workpiece mounting posture.

[0034] Furthermore, the mathematical expression for establishing the optimal toolpath model for the surface to be machined is:

[0035]

[0036]

[0037] Where η i =s i -c i α min ,α max β is the limit of the tool rake angle range. min ,β max This represents the limit of the tool's side deviation angle range.

[0038] Furthermore, the established mathematical model is solved using an external penalty function-based constraint optimization algorithm.

[0039] (III) Beneficial Effects

[0040] This invention provides a method for generating toolpaths for high-efficiency, low-acceleration multi-axis machining of complex curved surfaces. By constructing a new toolpath optimization objective, it simultaneously balances the contradictory relationship between surface machining efficiency and machine tool acceleration, enabling the machine tool to operate at both high machining efficiency and low acceleration to the greatest extent possible. This effectively achieves high area removal rate machining of complex curved surfaces under low acceleration. Compared to existing methods, this invention achieves lower machine tool acceleration for the same surface machining efficiency, or higher surface machining efficiency for the same machine tool acceleration, thus maximizing the simultaneous fulfillment of the objective requirements for high efficiency, high precision, and low-cost manufacturing of complex curved surface multi-axis machining. Attached Figure Description

[0041] Figure 1 This is a flowchart of a method for generating toolpaths for complex curved surfaces with high efficiency and low acceleration, as disclosed in this application.

[0042] Figure 2 This application discloses a surface partitioning diagram based on the normal vector case.

[0043] Figure 3 This is a surface and tool trajectory direction analysis diagram disclosed in this application.

[0044] Figure 4 This is a schematic diagram of one of the different processing trajectories disclosed in this application. Detailed Implementation

[0045] The present invention will now be described in detail with reference to the accompanying drawings, and the technical solutions in the embodiments of the present invention will be clearly and completely described. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0046] like Figure 1 This invention discloses a method for generating toolpaths for high-efficiency, low-acceleration multi-axis machining of complex curved surfaces, enabling high area removal rates during machining of complex curved surfaces under low acceleration. The main technical solution is as follows:

[0047] Step S1: Discretize the surface to be processed based on the surface normal vector to obtain the surface feature points;

[0048] First, based on the normal vector of the surface to be machined, the surface is discretized into n feature points using a discretization precision ε. The surface normal vector refers to the direction of the normal to a point on the surface, i.e., the direction perpendicular to the surface. Discretization transforms a continuous surface into a discrete set of points using a certain method. This is for processing in a computer, because the basic unit of computer processing is discrete pixels or points. The selection of these feature points and the establishment of the coordinate system take into account the normal direction of the surface, which helps to determine the tool feed direction and machining trajectory.

[0049] Step S2: Construct an objective function at each feature point to achieve high-efficiency, low-acceleration surface processing;

[0050] In multi-axis machining of complex surfaces, the objective function is a mathematical expression used to quantify and optimize important parameters during the machining process. By constructing objective functions, factors such as workpiece machining quality, machining efficiency, and machine tool operating status can be numerically evaluated, and more ideal machining results can be obtained by optimizing these objective functions.

[0051] Specifically, in step S2, the objective function achieves a balance and optimization of two key performance indicators:

[0052] 1. Efficiency of surface machining: The volume of material removed or the area machined per unit time. Efficient toolpath planning can reduce machining time and increase productivity.

[0053] 2. Low acceleration operation of machine tools: Maintaining a low acceleration can reduce machine tool wear and extend its service life. It also helps maintain stability during the machining process and avoids the impact of vibration caused by high acceleration on machining accuracy.

[0054] The ultimate goal of optimization is to optimize the objective function (i.e., local machining efficiency and acceleration) at each discrete feature point. From a global perspective, the purpose of the entire toolpath planning is to optimize the sum of the objective function values ​​at all discrete feature points, thereby achieving high-efficiency and low-acceleration machining of the entire surface.

[0055] Step S3: Establish a mathematical model for surface processing optimization, taking the sum of the objective functions at each feature point as the optimization objective;

[0056] Step S4: Solve the mathematical model using the constraint optimization method to obtain the optimal toolpath generation parameters;

[0057] Step S4 involves using constraint optimization methods to solve the established mathematical model. Constraint optimization is a type of mathematical problem that seeks variable values ​​that maximize or minimize the objective function while satisfying a set of constraints. In the context of surface machining, constraint optimization methods such as the external penalty function method can be used to solve the optimization mathematical model, thereby simultaneously obtaining the optimal surface machining trajectory, tool axis vector, and workpiece mounting posture, and solving for the parameter values ​​that optimize the objective function.

[0058] Step S5: Generate the machining toolpath for the surface to be machined based on the optimal toolpath generation parameters.

[0059] Based on the optimal toolpath generation parameters obtained in step S4, step S5 involves generating the actual toolpath required for machining the surface. The entire toolpath planning process is programmable, and the planned toolpath can achieve high area removal rate machining of complex surfaces under low acceleration. This step is completed using CAM (Computer-Aided Manufacturing) software, which converts the optimized parameters into command codes that the machine tool can understand and execute. Finally, these codes are uploaded to the CNC machine tool to guide the tool to move along the predetermined path, thereby machining the surface required by the design.

[0060] In this way, the method of the present invention can effectively balance processing efficiency and machine tool operation stability, thereby improving production efficiency and reducing costs while ensuring processing quality.

[0061] Please refer to Figures 2-4 The present invention implements the above embodiments in the following specific steps:

[0062] 1) For a given surface S, discretize it into a point set p = {p1, p2, ..., p...} with a given precision ε. i ,....p n}. And select any point p in the point set p. i , with point p i Let the origin be o, and let point p be... i The principal normal vector of the surface is the z-axis, and the tangent vector along the u-axis is the x-axis. Establish a local coordinate system oxyz with the y-axis as the coordinate axis.

[0063] 2) Rotate the xoz plane counterclockwise around the z-axis, and denote the rotation angle as θ. i The resulting plane of rotation is denoted as p-θ. i At this time, the plane p-θ i The intersection line with the given surface S to be processed is denoted as L. i Then in L i Above, with step size Δs at p i Take one point before and one point after, and denote them as follows: and

[0064] 3) At the acquisition point and points Then, based on the dual requirements of high efficiency and low acceleration in machining toolpaths, at point p... i Establish an objective function that can simultaneously achieve high efficiency and low acceleration processing to the greatest extent.

[0065] The following explanation will take an AB structure five-axis linkage machine tool as an example.

[0066] In p i The objective function of the toolpath optimization mathematical model corresponding to the point needs to consider two factors simultaneously: high cutting efficiency and low acceleration of the machine tool motion axis, that is, pursuing "high area removal rate" machining under "low acceleration". Therefore, at p... i Point target η i This can be expressed as follows:

[0067] η i =s i -c i

[0068] Where s i The representative item representing the processing area removal rate is defined as follows:

[0069] At a given feed rate λ, for a point p on the surface i Any machining direction θ, tool rake angle α, and tool sideslip angle β, p i Processing line width d i It is a function of θ, α, and β, and given a constant feed rate, the area s to be removed during processing... i With processing line width d i If they are directly proportional, then s i It is also a function of θ, α, and β, i.e., s i =s i (θ,α,β)=λ*d i (θ,α,β), the specific function expression can be calculated according to the shape of the specific machining tool.

[0070] Where c i The term representing machine tool acceleration is defined as follows:

[0071] High machine tool acceleration often means high machine tool wear and high energy consumption. It can be known that, given fixed cutting parameters, energy consumption c... ie and machine tool wear c im It is positively correlated with the acceleration of the machine tool's motion axis, therefore the energy consumption c can be easily established. ie and machine tool wear c im The relationship between the acceleration 'a' along each axis:

[0072] c ie +c im =ω i (m A a iA +m B a iB +m x a ix +m y a iy +m z a iz ).

[0073] Where, m A The A-axis at point p i The corresponding quality weighting coefficient, ω i The positive correlation coefficient, α iA The A-axis at point p i The corresponding acceleration can be calculated using the following formula:

[0074]

[0075] Where M = (X, Y, Z, A, B), and λ is the feed rate. Δs can be calculated using the following formula:

[0076]

[0077] Then the machine tool acceleration representative term c i It can be expressed as follows:

[0078] c i =ω i (m A α iA +m B α iB +m x α ix +m y α iy +m z α iz ).

[0079] From the motion transformation process of the five-axis machine tool post-processor, we can know that a iM (M=(X,Y,Z,A,B)) varies with the machining trajectory (θ), tool axis vector (α,β), and workpiece mounting posture (x,y,z,φ(x),φ(y),φ(z)). Therefore, a iM (M=(X,Y,Z,A,B)) can be represented as a function of machining trajectory (θ), tool axis vector (α,β), and workpiece mounting posture (x,y,z,φ(x),φ(y),φ(z)), then c iIt can also be expressed as a function of the machining trajectory (θ), the tool axis vector (α,β), and the workpiece mounting posture (x,y,z,φ(x),φ(y),φ(z)), i.e.:

[0080] c i =c i (θ,α,β,x,y,z,φ(x),φ(y),φ(z)).

[0081] From the above, we can see that the objective function η i It can be expressed as a function of (θ, α, β, x, y, z, φ(x), φ(y), φ(z)), i.e.

[0082] η i =η i (θ,α,β,x,y,z,φ(x),φ(y),φ(z)).

[0083] 4) The objective function of the entire surface toolpath optimization mathematical model can be represented by the sum of the objective functions of each feature point, i.e. The optimization variables can be selected based on the motion transformation process of the five-axis machine tool's post-processing, that is, the variables that affect the objective function value throughout the process. Therefore, this section uses the machining trajectory (θ), tool axis vector (α,β), and workpiece mounting posture (x,y,z,φ(x),φ(y),φ(z)) as the optimization variables of this mathematical model. The mathematical model for optimizing the toolpath of the surface to be machined is established as follows:

[0084]

[0085]

[0086] The objective function η can be derived from the point set p = {p1, p2, ..., p...} i ,....p n The corresponding target η i The sum represents α. min ,α max β is the limit of the tool rake angle range. min ,β max This represents the limit of the tool's side deviation angle range.

[0087] 5) Solve the mathematical model in step 4) using constraint optimization algorithms such as external penalty functions to obtain the θ corresponding to the maximum η. * ,α * ,β * ,x * ,y * ,z * ,φ(x) * ,φ(y) * ,φ(z) *This means obtaining the optimal surface machining trajectory, tool axis vector, and workpiece mounting posture.

[0088] 6) Take any point p on the surface S, with θ * Determine the surface machining trajectory, with α * ,β * Determine the tool axis vector, and based on x * ,y * ,z * ,φ(x) * ,φ(y) * ,φ(z) * Determine the workpiece's mounting orientation on the machine tool. This allows for the generation of the machining trajectory for the entire surface to be machined. The generated toolpath enables machining with a high area removal rate at low acceleration.

[0089] This method discretizes surface feature points and constructs an optimization objective function aimed at maximizing high-efficiency, low-acceleration surface machining. A mathematical model for surface machining optimization is established using toolpath, tool axis vector, and workpiece mounting posture as optimization variables. This model is solved using a constrained optimization algorithm to obtain the optimal surface machining trajectory, tool axis vector, and workpiece mounting posture. The optimization mathematical model considers both high cutting efficiency and low machine tool axis acceleration, enabling the generated toolpath to achieve a high area removal rate under low acceleration. The entire process is programmable, and the generated toolpath can be applied to complex surface machining to achieve high-efficiency, low-acceleration machining results.

[0090] The above embodiments are only used to illustrate the technical solutions of this application and are not intended to limit it. Although this application has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of this application without departing from the spirit and scope of the technical solutions of this application.

Claims

1. A method for generating toolpaths for high-efficiency, low-acceleration multi-axis machining of complex curved surfaces, characterized in that, Includes the following steps: Discretize the surface to be processed based on the surface normal vector to obtain the surface feature points; Construct an objective function at each feature point to achieve high-efficiency, low-acceleration surface processing; A mathematical model for surface processing optimization is established, taking the sum of the objective functions at each feature point as the optimization objective. The mathematical model was solved using a constrained optimization method to obtain the optimal parameters for toolpath generation. The machining toolpath for the surface to be machined is generated based on the optimal toolpath generation parameters; the step of constructing the objective function at each feature point to achieve high-efficiency, low-acceleration machining of the surface includes: feature points Let the origin be the point. The principal normal vector of the surface is the z-axis, and the tangent vector along the u-axis is the x-axis. Establish a local coordinate system oxyz with the y-axis as the coordinate axis; Rotate the xoz plane counterclockwise around the z-axis by the angle denoted as . To obtain the plane of rotation Rotation plane The intersection line with the given surface S to be processed is denoted as ; exist Up, with step length exist Take one point before and one point after, and denote them as follows: and ; Based on the requirements of high efficiency and low acceleration in machining toolpaths, at point Establish the objective function to achieve high-efficiency, low-acceleration machining. ; at point In the step of establishing the objective function to achieve high-efficiency, low-acceleration machining, the objective function... Represented as ,in Indicates the removal rate of the processed area. This represents the acceleration of the machine tool.

2. The method for generating toolpaths for high-efficiency, low-acceleration multi-axis machining of complex curved surfaces according to claim 1, characterized in that, in This indicates that, given a feed rate λ, for a point on the surface... Arbitrary machining direction Tool tilt angle and the tool side angle , Processing line width yes , as well as The function, that is: 。 3. The method for generating toolpaths for high-efficiency, low-acceleration multi-axis machining of complex curved surfaces according to claim 2, characterized in that, in The representative term of machine tool acceleration is defined as follows: ， in, The positive correlation coefficient The A-axis at point The corresponding quality weighting coefficient, The A-axis at point The corresponding acceleration; The B-axis at point The corresponding quality weighting coefficient, The B-axis at point The corresponding acceleration; The x-axis at point The corresponding quality weighting coefficient, The x-axis at point The corresponding acceleration; The y-axis at point The corresponding quality weighting coefficient, The y-axis at point The corresponding acceleration; The z-axis at point The corresponding quality weighting coefficient, The z-axis at point The corresponding acceleration.

4. The method for generating toolpaths for high-efficiency, low-acceleration multi-axis machining of complex curved surfaces according to claim 3, characterized in that, in It is expressed as a function of machining trajectory (θ), tool axis vector (α, β), and workpiece mounting posture (x, y, z, φ(x), φ(y), φ(z)), i.e.: 。 5. The method for generating toolpaths for high-efficiency, low-acceleration multi-axis machining of complex curved surfaces according to claim 1, characterized in that, In the step of constructing the mathematical model for surface machining optimization, the optimization variables include the surface machining trajectory, the tool axis vector, and the workpiece mounting posture.

6. The method for generating toolpaths for high-efficiency, low-acceleration multi-axis machining of complex curved surfaces according to claim 4, characterized in that, The mathematical expression for establishing the toolpath optimization mathematical model for the surface to be machined is: in, Max The optimal objective function for the mathematical model of surface toolpath optimization is... , This represents the limit of the tool's rake angle range. This represents the limit of the tool's side deviation angle range.

7. The method for generating toolpaths for high-efficiency, low-acceleration multi-axis machining of complex curved surfaces according to claim 1, characterized in that, The established mathematical model is solved using an external penalty function method-constrained optimization algorithm.

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