Cutter positioning method and system in multi-axis machine tool simulation process

Abstract

The invention discloses a tool positioning method and system in a multi-axis machine tool simulation process, and the method comprises the steps: employing a quaternion virtual tool kinematics model, describing a tool posture based on a real part quantity and virtual part quantity representation method, and building a tool position transformation matrix containing rotation and translation information; a non-uniform rational B-spline curve is adopted to describe the surface features of the workpiece, the curvature factor of the surface of the workpiece is calculated according to an adaptive grid division algorithm, and the grid density is dynamically adjusted according to the curvature factor; the minimum distance between the tool surface point set and the workpiece surface point set is calculated, whether interference occurs between the tool and the workpiece surface or not is judged, and interference point position information is recorded; high precision, high efficiency and high reliability of tool positioning in the multi-axis machine tool machining simulation process are achieved, the actual machining cost can be effectively reduced, the trial cutting frequency is reduced, and the reliability of the machining procedure is improved.

Description

Technical Field

[0001] The invention belongs to the technical field of numerical control machining, and in particular relates to a tool positioning method and system in a multi-axis machine tool simulation process. Background Art

[0002] The problem of tool positioning in multi-axis CNC machining has always been a technical difficulty in this field, mainly due to the complexity of the tool kinematic description. The traditional Euler angle method has singularity problems when describing the tool posture, the coupling relationship between tool position and posture is difficult to express accurately, and the kinematic transformation calculation in the multi-axis linkage process is complex. When modeling the workpiece surface, the conventional discrete point method is difficult to accurately describe the complex surface, the traditional interference detection algorithm has a large amount of calculation, and it is easy to miss the detection in the complex surface processing, and the interference point information is difficult to accurately record and trace. Summary of the invention

[0003] In view of the above problems, the present invention proposes a tool kinematic model based on quaternions and a workpiece surface description method based on non-uniform rational B-spline curves, combined with an adaptive meshing algorithm, to achieve efficient and accurate tool positioning and interference detection. The specific technical solutions are as follows:

[0004] In a first aspect, the present invention provides a tool positioning method in a multi-axis machine tool simulation process, the method comprising the following steps:

[0005] Step S1, using a quaternion virtual tool kinematics model, describing the tool posture based on a representation method of real component plus imaginary component, and establishing a tool position transformation matrix containing rotation and translation information.

[0006] The tool posture It is expressed as: ,in, represents the real component of the quaternion, , is the rotation angle of the tool around the rotation axis; , , Represents the imaginary component of the quaternion, which represents the tool around the machine tool , , The component of the axis rotation, , , Respectively represent machine tools , , Three orthogonal basis directions imaginary units; The real and imaginary components satisfy the following constraint equations: , in, , , The rotation axis is , , The unit component of the direction; Step S2, using a non-uniform rational B-spline curve to describe the workpiece surface features, calculating the workpiece surface curvature factor according to an adaptive meshing algorithm, and dynamically adjusting the mesh density according to the curvature factor; The method of using non-uniform rational B-spline curves to describe the surface features of the workpiece includes: Create a control point grid ,in, , They are , The number of control points in the direction, Represents the tool direction parameter of the workpiece, with a definition domain of [0,1], Represents the feed direction parameter of the workpiece, with a definition domain of [0,1]; Set the weight factor corresponding to each control point ,calculate Step and Step Spline basis function, calculate the workpiece surface points The curvature factor at ; Step S3, calculating the minimum distance between the tool surface point set and the workpiece surface point set, determining whether interference occurs between the tool and the workpiece surface, and recording the interference point position information.

[0007] Furthermore, the tool position transformation matrix The calculation formula is: , in , , is the coordinate value of the tool reference point in the workpiece coordinate system. The upper left 3×3 submatrix of the matrix represents the rotation transformation of the tool. The transpose of the rightmost column vector Represents a translation transformation.

[0008] Furthermore, the non-uniform rational B-spline curve is used to describe the surface features of the workpiece. The mathematical expression is: ;in, They are Direction The order of the spline basis function; , for Direction control point index, ; for Direction control point index, ; The control point grid size is ; and Respectively Basis function matrix of direction and The elements of , where: ; ; Real-time position of control points during simulation , the weight matrix , then the transformed workpiece surface features The mathematical expression is: ;in, is the control point matrix.

[0009] Furthermore, the The basis functions of the directions are defined recursively, where: ; ; is the node vector Node value.

[0010] Furthermore, the workpiece surface curvature factor is calculated according to the adaptive meshing algorithm, and the mesh density is dynamically adjusted according to the curvature factor. The curvature factor at , then point The mesh density at for: , in: is the base grid density, , is the minimum machining accuracy required; is the density adjustment coefficient, the value range is [0,1], the curvature factor The calculation formula is: , in is the maximum principal curvature, is the minimum principal curvature.

[0011] Furthermore, the minimum distance calculation for interference detection adopts: , in, Represents the position transformation matrix The transformed tool surface point set, is the sampling point on the tool surface, and its coordinates are transformed by the position matrix Calculated, ,in is the point in the tool's original coordinate system; Represented by non-uniform rational B-spline curve The surface point set of the workpiece described by is the sampling point on the workpiece surface; Represents the Euclidean distance between two points in space; Interference is determined to occur when the following conditions are met: , Interference judgment threshold, the value is not greater than the minimum processing accuracy .

[0012] Furthermore, the recorded position information of the interference point is the corresponding tool position quaternion and the corresponding workpiece surface coordinate parameters when the interference occurs.

[0013] In a second aspect, the present invention provides a tool positioning system in a multi-axis machine tool simulation process, which is used to execute a tool positioning method in a multi-axis machine tool simulation process described in the first aspect, and the system includes: a kinematic modeling module, a surface modeling module and an interference detection module connected in sequence.

[0014] Furthermore, the kinematic modeling module is used to adopt a quaternion virtual tool kinematic model, describe the tool posture based on the representation method of real component plus imaginary component, and establish a tool position transformation matrix containing rotation and translation information.

[0015] Furthermore, the surface modeling module is used to describe the surface features of the workpiece using non-uniform rational B-spline curves, calculate the curvature factor of the workpiece surface according to an adaptive meshing algorithm, and dynamically adjust the mesh density according to the curvature factor.

[0016] Furthermore, the interference detection module is used to calculate the minimum distance between the tool surface point set and the workpiece surface point set, determine whether interference occurs between the tool and the workpiece surface, and record the position information of the interference point.

[0017] Furthermore, the system also includes: a data management module, a visualization module and a parameter configuration module.

[0018] The data management module is used to manage data during the operation of the system, including: a control point database for storing the control point grid and weight factors of the workpiece surface; a tool parameter library for storing tool geometric parameters and motion parameters; and an interference record library for storing detected interference point information.

[0019] The visualization module is used to display the tool motion trajectory, workpiece surface mesh and interference detection results in real time.

[0020] The parameter configuration module is used to set the minimum processing accuracy of the simulation system. , grid density adjustment coefficient , and the interference determination threshold .

[0021] Compared with the prior art, the present invention has the following beneficial effects: The present invention adopts quaternions to represent tool posture, thus avoiding the singularity problem in the traditional Euler angle representation method, and ensures numerical stability through constraint equations of real and imaginary components, thereby improving the accuracy and computational efficiency of tool kinematic modeling; adopts non-uniform rational B-spline curves to describe the workpiece surface, combined with an adaptive grid division algorithm based on curvature factor, thereby realizing dynamic adjustment of grid density, thereby improving computational efficiency while ensuring accuracy; improves detection reliability through flexible setting of interference judgment threshold and accurate recording of interference point position information; the present invention realizes high-precision, high-efficiency and high-reliability tool positioning in the process of multi-axis machine tool machining simulation, thereby effectively reducing actual machining costs, reducing the number of trial cutting times, and improving the reliability of machining procedures. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 The present invention is a flow chart of a tool positioning method in a multi-axis machine tool simulation process.

[0023] Figure 2 The present invention is a schematic diagram of the composition of a tool positioning system in a multi-axis machine tool simulation process. DETAILED DESCRIPTION

[0024] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention is described clearly and completely below. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0025] Example 1 like Figure 1 As shown, a tool positioning method in a multi-axis machine tool simulation process of the present invention is shown, and the method comprises the following steps: Step S1, using a quaternion virtual tool kinematics model, describing the tool posture based on a representation method of real component plus imaginary component, and establishing a tool position transformation matrix containing rotation and translation information.

[0026] The tool posture It is expressed as: ,in, represents the real component of the quaternion, , is the rotation angle of the tool around the rotation axis; , , Represents the imaginary component of the quaternion, which represents the tool around the machine tool , , The component of the axis rotation, , , Respectively represent machine tools , , Three orthogonal basis directions imaginary units; The real and imaginary components satisfy the following constraint equations: , in, , , The rotation axis is , , The unit component of the direction.

[0027] It should be noted that Represents the real component of the quaternion, which represents half of the cosine value of the rotation angle; any posture of the tool can be uniquely determined by this quaternion, avoiding the gimbal lock problem in the traditional Euler angle representation; Here is a quaternion representation of the tool posture, for example, when the tool is rotated 90 degrees around the X axis: When the tool is rotated 90 degrees around the X axis: .

[0028] When the tool is rotated 90 degrees around the Y axis: .

[0029] When the tool is rotated 90 degrees around the Z axis: .

[0030] The rotation angle is half (45°) because quaternions represent rotations, which simplifies calculations during continuous rotations.

[0031] The tool position transformation matrix The calculation formula is: , in , , is the coordinate value of the tool reference point in the workpiece coordinate system. The upper left 3×3 submatrix of the matrix represents the rotation transformation of the tool. The transpose of the rightmost column vector Represents a translation transformation.

[0032] Step S2, using non-uniform rational B-spline curves to describe the workpiece surface features, calculating the workpiece surface curvature factor according to an adaptive meshing algorithm, and dynamically adjusting the mesh density according to the curvature factor.

[0033] The method of using non-uniform rational B-spline curves to describe the surface features of the workpiece includes: Create a control point grid ,in, , They are , The number of control points in the direction, Represents the tool direction parameter of the workpiece, with a definition domain of [0,1], Represents the feed direction parameter of the workpiece, with a definition domain of [0,1]; Set the weight factor corresponding to each control point ,calculate Step and Step Spline basis function, calculate the workpiece surface points The curvature factor at ; The non-uniform rational B-spline curve is used to describe the surface features of the workpiece The mathematical expression is: ;in, They are Direction The order of the spline basis function; , for Direction control point index, ; for Direction control point index, ; The control point grid size is ; and Respectively Basis function matrix of direction and The elements of , where: ; ; Real-time position of control points during simulation , the weight matrix , then the transformed workpiece surface features The mathematical expression is: ;in, is the control point matrix.

[0034] Set the weight factor corresponding to each control point. The weight factor is a positive real number that represents the influence of the control point on the surface shape. The larger the value, the closer the surface is to the control point. =1 indicates uniform influence. The principle of adjusting the weight factor is: when certain features need to be strengthened, increase the weight of the corresponding control point, and appropriately reduce the weight of the control points in unimportant areas. The weight value range is between 0.1 and 10.

[0035] Said The basis functions of the directions are defined recursively, where: ; ; is the node vector Node value.

[0036] The workpiece surface curvature factor is calculated according to the adaptive meshing algorithm, and the mesh density is dynamically adjusted according to the curvature factor. The curvature factor at , then point The mesh density at for: , in: is the base grid density, , is the minimum machining accuracy required; is the density adjustment coefficient, the value range is [0,1], the curvature factor The calculation formula is: , in is the maximum principal curvature, is the minimum principal curvature.

[0037] Step S3, calculating the minimum distance between the tool surface point set and the workpiece surface point set, determining whether interference occurs between the tool and the workpiece surface, and recording the interference point position information.

[0038] The minimum distance calculation for interference detection is: , in, Represents the position transformation matrix The transformed tool surface point set, is the sampling point on the tool surface, and its coordinates are transformed by the position matrix Calculated, ,in is the point in the tool's original coordinate system; Represented by non-uniform rational B-spline curve The surface point set of the workpiece described by is the sampling point on the workpiece surface; Represents the Euclidean distance between two points in space; Interference is determined to occur when the following conditions are met: , Interference judgment threshold, the value is not greater than the minimum processing accuracy .

[0039] The recorded position information of the interference point is the corresponding tool position quaternion and the corresponding workpiece surface coordinate parameters when the interference occurs.

[0040] This embodiment also provides intelligent optimization of the simulation process, establishes a simulation parameter adaptive adjustment mechanism, and defines a simulation quality evaluation index Q: in, is the position accuracy indicator, , is the actual location, is the theoretical position, is the attitude accuracy index, , is the actual angle, From a theoretical perspective; is the computational efficiency index, , is the current calculation time, Base time* is the weight coefficient and satisfies .

[0041] Construct a parameter optimization model and optimize the objective function: , is the Lagrange multiplier; design an intelligent optimization algorithm and use the gradient descent method to update the parameters: in, is the parameter value of the kth iteration, is the learning rate, ranging from [0.01, 0.1], The partial derivative of the objective function with respect to the parameter is used to establish a simulation quality feedback mechanism to monitor key indicators in real time: tool position deviation , attitude angle deviation , calculation time consumption .

[0042] Example 2 like Figure 2 As shown, it is a schematic diagram of the composition of a tool positioning system in a multi-axis machine tool simulation process of the present invention, which is used to execute a tool positioning method in a multi-axis machine tool simulation process described in Example 1. The system includes: a kinematic modeling module, a surface modeling module and an interference detection module connected in sequence.

[0043] The kinematic modeling module is used to describe the tool posture based on the representation method of real component plus imaginary component using a virtual tool kinematic model of quaternion, and to establish a tool position transformation matrix containing rotation and translation information; The surface modeling module is used to describe the surface features of the workpiece using a non-uniform rational B-spline curve, calculate the curvature factor of the workpiece surface according to an adaptive meshing algorithm, and dynamically adjust the mesh density according to the curvature factor; The interference detection module is used to calculate the minimum distance between the tool surface point set and the workpiece surface point set, determine whether interference occurs between the tool and the workpiece surface, and record the interference point position information.

[0044] The above three modules constitute the core module of the system. In addition, the system also includes: a data management module, a visualization module and a parameter configuration module; which are respectively connected to the core module.

[0045] The data management module is used to manage the data during the operation of the system, including: a control point database for storing the control point grid and weight factors of the workpiece surface; a tool parameter library for storing tool geometric parameters and motion parameters; and an interference record library for storing detected interference point information; The visualization module is used to display the tool motion trajectory, workpiece surface mesh and interference detection results in real time; The parameter configuration module is used to set the minimum processing accuracy of the simulation system. , grid density adjustment coefficient , and the interference determination threshold .

[0046] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A tool positioning method in a multi-axis machine tool simulation process, characterized in that: The method comprises the following steps: Step S1, using a quaternion virtual tool kinematic model, describing the tool posture based on a representation method of real component plus imaginary component, and establishing a tool position transformation matrix containing rotation and translation information; The tool posture It is expressed as: ,in, represents the real component of the quaternion, , is the rotation angle of the tool around the rotation axis; , , Represents the imaginary component of the quaternion, which represents the tool around the machine tool , , The component of the axis rotation, , , Respectively represent machine tools , , Three orthogonal basis directions imaginary units; The real and imaginary components satisfy the following constraint equations: ， in, , , The rotation axis is , , The unit component of direction; Step S2, using a non-uniform rational B-spline curve to describe the workpiece surface features, calculating the workpiece surface curvature factor according to an adaptive meshing algorithm, and dynamically adjusting the mesh density according to the curvature factor; The method of using non-uniform rational B-spline curves to describe the surface features of the workpiece includes: Create a control point grid ,in, , They are , The number of control points for the direction, Represents the tool direction parameter of the workpiece, with a definition domain of [0,1], Represents the feed direction parameter of the workpiece, with a definition domain of [0,1]; Set the weight factor corresponding to each control point ,calculate Step and Step Spline basis function, calculate the workpiece surface points The curvature factor at ; Step S3, calculating the minimum distance between the tool surface point set and the workpiece surface point set, determining whether interference occurs between the tool and the workpiece surface, and recording the interference point position information.

2. The tool positioning method in a multi-axis machine tool simulation process according to claim 1, characterized in that: The tool position transformation matrix The calculation formula is: ， in , , is the coordinate value of the tool reference point in the workpiece coordinate system. The upper left 3×3 submatrix of the matrix represents the rotation transformation of the tool. The transpose of the rightmost column vector Represents a translation transformation.

3. The tool positioning method in a multi-axis machine tool simulation process according to claim 2, characterized in that: The non-uniform rational B-spline curve is used to describe the surface features of the workpiece The mathematical expression is: ;in, They are Direction The order of the spline basis function; , for Direction control point index, ; for Direction control point index, ; The control point grid size is ; and Respectively Basis function matrix of direction and The elements of , where: ； ； Real-time position of control points during simulation , the weight matrix , then the transformed workpiece surface features The mathematical expression is: ;in, is the control point matrix.

4. The tool positioning method in a multi-axis machine tool simulation process according to claim 3, characterized in that: Said The basis functions of the directions are defined recursively, where: ; ; is the node vector Node value.

5. The tool positioning method in a multi-axis machine tool simulation process according to claim 4, characterized in that: The workpiece surface curvature factor is calculated according to the adaptive meshing algorithm, and the mesh density is dynamically adjusted according to the curvature factor. The curvature factor at , then point The mesh density at for: ， in: is the base grid density, , is the minimum machining accuracy required; is the grid density adjustment coefficient, the value range is [0,1], the curvature factor The calculation formula is: ， in is the maximum principal curvature, is the minimum principal curvature.

6. The tool positioning method in a multi-axis machine tool simulation process according to claim 5, characterized in that: The minimum distance calculation for interference detection is: ， in, Represents the position transformation matrix The transformed tool surface point set, is the sampling point on the tool surface, and its coordinates are transformed by the position matrix Calculated, ,in is the point in the tool's original coordinate system; Represented by non-uniform rational B-spline curve The surface point set of the workpiece described by is the sampling point on the workpiece surface; Represents the Euclidean distance between two points in space; Interference is determined to occur when the following conditions are met: , Interference judgment threshold, the value is not greater than the minimum processing accuracy .

7. The tool positioning method in a multi-axis machine tool simulation process according to claim 5, characterized in that: The recorded position information of the interference point is the corresponding tool position quaternion and the corresponding workpiece surface coordinate parameters when the interference occurs.

8. A tool positioning system in a multi-axis machine tool simulation process, used to execute a tool positioning method in a multi-axis machine tool simulation process according to any one of claims 1 to 7, characterized in that: The system comprises: a kinematics modeling module, a surface modeling module and an interference detection module connected in sequence; The kinematic modeling module is used to describe the tool posture based on the representation method of real component plus imaginary component using a virtual tool kinematic model of quaternion, and to establish a tool position transformation matrix containing rotation and translation information; The surface modeling module is used to adopt non-uniform rational The spline curve describes the workpiece surface features, the workpiece surface curvature factor is calculated according to the adaptive meshing algorithm, and the mesh density is dynamically adjusted according to the curvature factor; The interference detection module is used to calculate the minimum distance between the tool surface point set and the workpiece surface point set, determine whether interference occurs between the tool and the workpiece surface, and record the interference point position information.

9. A tool positioning system in a multi-axis machine tool simulation process according to claim 8, characterized in that: The system also includes: a data management module, a visualization module and a parameter configuration module; The data management module is used to manage the data during the operation of the system, including: a control point database for storing the control point grid and weight factors of the workpiece surface; a tool parameter library for storing tool geometric parameters and motion parameters; and an interference record library for storing detected interference point information; The visualization module is used to display the tool motion trajectory, workpiece surface mesh and interference detection results in real time; The parameter configuration module is used to set the minimum processing accuracy of the simulation system. , grid density adjustment coefficient , and the interference determination threshold .

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