A machining trajectory interpolation method for five-axis CNC

Abstract

The present application provides a five-axis CNC machining trajectory interpolation method, which relates to the field of CNC machining technology, including: extracting the denture machining contour; obtaining the denture contour NURBS parameter curve; deriving the homogeneous coordinate expression of the NURBS parameter curve in N-dimensional space; obtaining the coordinates of each point on the denture contour NURBS parameter curve, and calculating the curve length using a numerical analysis algorithm; for the denture contour NURBS parameter curve, calculating the derivative vector on the curve, and determining the curvature change of the curve at the interpolation point; locating the interpolation point coordinates according to the curve length and the derivative vector, and using the interpolation point coordinates for machining path planning. The present application can solve the technical problem of poor machining accuracy due to the uneven machining trajectory in the prior art, thereby improving the machining quality, significantly reducing the machining time and cost, and meeting the technical effect of high precision and high efficiency requirements for denture manufacturing.

Description

Technical Field

[0001] The present application relates to the technical field of numerical control machining, and in particular to a machining trajectory interpolation method for five-axis numerical control. Background Art

[0002] With the development of modern oral restoration technology, the requirements for precision and surface quality in denture manufacturing are increasing. The complex shape and fine contours of dentures make it difficult for traditional processing methods to meet the high-precision and high-efficiency processing needs.

[0003] Due to the complex and changeable morphology of teeth, according to the analysis of the processing trajectory, it is found that denture processing belongs to the type of continuous short straight line segment processing, which contains a large number of short straight line segment (less than 1mm in length) commands, and there are a large number of small arcs and sharp turning points. A large number of sudden turning points need to be processed during the interpolation process, resulting in an uneven processing trajectory and difficulty in achieving high-speed processing. The speed control method of traditional CNC machine tools is to reduce the feed speed to zero at the turning point of linear processing, resulting in frequent machine tool start and stop, causing the machine tool to vibrate and reduce the processing accuracy. In order to improve the accuracy and speed of processing, it is very important to study effective interpolation algorithms.

[0004] In summary, the prior art has a technical problem of poor machining accuracy due to an uneven machining trajectory. Summary of the invention

[0005] The purpose of this application is to provide a five-axis CNC machining trajectory interpolation method to solve the technical problem in the prior art that the machining trajectory is not smooth, resulting in poor machining accuracy.

[0006] In view of the above problems, the present application provides a five-axis CNC machining trajectory interpolation method, including: collecting target structure information of the denture and extracting the denture machining contour; based on the denture machining contour, performing curve fitting through the NURBS parameter curve to obtain the denture contour NURBS parameter curve; using aligned coordinates to represent the denture contour NURBS parameter curve, and deriving the homogeneous coordinate expression of the NURBS parameter curve in N-dimensional space; according to the homogeneous coordinate expression, obtaining the coordinates of each point on the denture contour NURBS parameter curve, and calculating the curve length using a numerical analysis algorithm; for the denture contour NURBS parameter curve, calculating the derivative vector on the curve, and determining the curvature change of the curve at the interpolation point; according to the curve length and the derivative vector, locating the interpolation point coordinates, and using the interpolation point coordinates to plan the machining path.

[0007] One or more technical solutions provided in this application have at least the following technical effects or advantages:

[0008] The target structure information of the denture is collected to extract the denture processing contour; based on the denture processing contour, the curve fitting is performed through the NURBS parameter curve to obtain the denture contour NURBS parameter curve; the denture contour NURBS parameter curve is represented by the alignment coordinates, and the homogeneous coordinate expression of the NURBS parameter curve in N-dimensional space is derived; according to the homogeneous coordinate expression, the coordinates of each point on the denture contour NURBS parameter curve are obtained, and the curve length is calculated using the numerical analysis algorithm; for the denture contour NURBS parameter curve, the derivative vector on the curve is calculated to determine the curvature change of the curve at the interpolation point; according to the curve length and the derivative vector, the interpolation point coordinates are located, and the processing path planning is performed using the interpolation point coordinates. By locating the interpolation point based on the derivative vector and curvature change of the NURBS curve, the density of the interpolation point is dynamically adjusted, and the processing path planning is performed. The processing path finally generated can ensure that the tool moves smoothly along the denture contour, thereby improving the processing quality, significantly reducing the processing time and cost, and meeting the technical effect of high precision and high efficiency requirements of denture manufacturing.

[0009] The above description is only an overview of the technical solution of the present application. In order to more clearly understand the technical means of the present application, it can be implemented according to the contents of the specification, and in order to make the above and other purposes, features and advantages of the present application more obvious and easy to understand, the specific implementation methods of the present application are specifically cited below. It should be understood that the content described in this section is not intended to identify the key or important features of the embodiments of the present application, nor is it intended to limit the scope of the present application. Other features of the present application will become easy to understand through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] In order to more clearly illustrate the technical solutions in the present application or the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings in the following description are only exemplary, and for ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying any creative work.

[0011] Figure 1 A schematic diagram of a process flow of a five-axis CNC machining trajectory interpolation method for this application;

[0012] Figure 2 A schematic diagram of a process flow for obtaining a homogeneous coordinate expression in a five-axis CNC machining trajectory interpolation method of the present application. DETAILED DESCRIPTION

[0013] This application solves the technical problem of poor machining accuracy due to uneven machining trajectory in the prior art by providing a five-axis CNC machining trajectory interpolation method. By positioning the interpolation points based on the derivative vector and curvature change of the NURBS curve, the density of the interpolation points is dynamically adjusted to plan the machining path. The resulting machining path can ensure that the tool moves smoothly along the denture contour, thereby improving the machining quality, significantly reducing the machining time and cost, and meeting the technical effect of high precision and high efficiency requirements for denture manufacturing.

[0014] Below, the technical solutions in the present application will be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all of the embodiments of the present application. It should be understood that the present application is not limited to the example embodiments described herein. Based on the embodiments of the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present application. It should also be noted that, for the convenience of description, only the parts related to the present application are shown in the accompanying drawings, rather than all of them.

[0015] Please see attached Figure 1 The present application provides a five-axis CNC machining trajectory interpolation method, which specifically includes the following steps:

[0016] Step 1: Collect the target structure information of the denture and extract the denture processing contour.

[0017] Specifically, the target structural information of the denture includes the shape, size, surface features, tooth arrangement, etc. of the denture, which is usually obtained through high-precision digital scanning technology, such as existing 3D scanning or CT scanning. The three-dimensional point cloud data or digital model (such as STL format) obtained by scanning will provide the target structural information. After obtaining the target structural information of the denture, it is necessary to post-process it to extract the contour information required for processing. The processing contour usually refers to the specific shape and size data required in the processing process, including various cutting paths, angles, straight line segments, curves and other information. Common methods include surface segmentation, boundary extraction and other technologies. For example, the cutting and clustering algorithms of point cloud data can be used to separate the feature areas in the three-dimensional model and extract clear processing contours.

[0018] Step 2: Based on the denture processing contour, curve fitting is performed through the NURBS parameter curve to obtain the denture contour NURBS parameter curve.

[0019] Specifically, NURBS curve is a mathematical representation method widely used in computer-aided design and computer graphics. It can flexibly represent various complex geometric shapes. NURBS curve can accurately fit complex geometric shapes, including straight lines, arcs and more complex free shapes, through control points, weights and node vectors. Therefore, it is suitable for representing complex and curved structures such as dentures.

[0020] In practical applications, the denture machining contour is used to fit the points on the denture machining contour using the NURBS fitting algorithm. The steps of this process are usually as follows: extract key feature points or contour boundaries from the denture machining contour, select appropriate control points through the existing NURBS curve fitting software, and generate NURBS curves based on these control points. By optimizing the fitting process, the control points and node vectors are adjusted to make the fitting curve as consistent as possible with the actual denture contour. The outer contour of the denture usually contains multiple curved parts. Traditional polynomial curve fitting may not be able to accurately represent these complex shapes, but through NURBS curve fitting, each curve segment can be accurately fitted according to the position and weight of the control points, thereby obtaining a smooth and accurate contour. The final denture contour NURBS parameter curve can efficiently describe the complex geometric shape of the denture and provide accurate trajectory planning for subsequent CNC machining.

[0021] Step 3: Use alignment coordinates to represent the denture contour NURBS parameter curve, and derive a homogeneous coordinate expression of the NURBS parameter curve in N-dimensional space.

[0022] Specifically, NURBS parametric curves are usually described by control points, weights, node vectors and orders. The homogeneous coordinate representation of NURBS curves is a way to enhance curve expression, especially in high-dimensional space, it can effectively express and process the geometric relationship between curves and surfaces. After fitting the denture contour with NURBS curves, the denture contour NURBS parametric curve is represented in an appropriate coordinate system. The purpose of aligning the coordinates is to ensure that the position and direction of the fitted curve in the geometric space meet the actual processing requirements. Homogeneous coordinates are a mathematical representation commonly used in computer graphics and geometry to process geometric transformations. In a homogeneous coordinate system, a point in an N-dimensional space can be represented by adding an additional dimension. For example, a two-dimensional point (x, y) can be represented as (x, y, 1) in a homogeneous coordinate system, and a three-dimensional point (x, y, z) can be represented as (x, y, z, 1), etc. In NURBS curves, control points and weights will be expanded to homogeneous coordinates for more efficient geometric transformations and calculations. In this way, the representation of NURBS curves can not only accurately reflect the geometric contours of the denture, but also perform various transformations in multi-dimensional space to adapt to complex processing and design requirements.

[0023] Step 4: According to the homogeneous coordinate expression, the coordinates of each point on the NURBS parameter curve of the denture contour are obtained, and the length of the curve is calculated using a numerical analysis algorithm.

[0024] Specifically, according to the homogeneous coordinate expression, a series of discrete values ​​of the parameter u are selected, the coordinates of each point are calculated, the coordinates corresponding to each parameter are calculated, and then the discrete interpolation points are determined. The NURBS parametric curve is discretely integrated, and the distance between the discrete interpolation points is accumulated to approximate the length of the curve. The derivative vector is calculated to obtain the length of the curve. This method can ensure that in the processing of complex denture surfaces, the generated interpolation points accurately reflect the shape of the curve.

[0025] Step 5: For the denture contour NURBS parameter curve, calculate the derivative vector on the curve to determine the curvature change of the curve at the interpolation point.

[0026] Specifically, in the NURBS parametric curve processing of the denture contour, calculating the derivative vector of the curve to determine the curvature change of the interpolation point is a key step. The derivative vector can describe the direction and rate of change of the curve at each interpolation point, where the first-order derivative provides the tangent direction and the second-order derivative describes the acceleration, that is, the rate at which the curve bends. Through these derivatives, the curvature of the curve at each interpolation point can be obtained, that is, the degree of curvature of the curve at different positions. The greater the curvature, the more severe the curvature of the area, and more interpolation points are required to maintain the smoothness and processing accuracy of the path; when the curvature is small, the interpolation points can be reduced to improve processing efficiency. The density of interpolation points is dynamically adjusted according to the change in curvature, so that the processing path is both accurate and efficient, thereby meeting the complex shape and high precision requirements of the denture.

[0027] Step six: Locate the interpolation point coordinates according to the curve length and the derivative vector, and use the interpolation point coordinates to plan the processing path.

[0028] Specifically, in the denture processing path planning, the distribution of interpolation points is first determined based on the curve length and derivative vector. The curve length is used to divide the path as a whole to ensure that the path segment length matches the processing requirements. The derivative vector represents the change in direction of the curve at each point. By calculating the derivative vector, the curvature distribution can be obtained to help locate the coordinates of interpolation points that require higher precision. Dense interpolation points are distributed in areas with larger curvatures to ensure the smoothness and accuracy of the processing path at sharp turns. Finally, all interpolation point coordinates are connected into a continuous path for tool control of CNC machine tools, so that the tool moves along a precise trajectory to meet the complex contours and surface quality requirements of dentures.

[0029] Further, as attached Figure 2 As shown, step three of this application includes:

[0030] Combine the control point di and the weight wi of the corresponding control point to obtain the weighted control point: Di=[wi,di,wi]; use the weighted control point to obtain the B-spline parametric curve in the n+1-dimensional space; project the B-spline parametric curve in the n+1-dimensional space onto the hyperplane of w=1 to obtain the homogeneous coordinate expression of the NURBS parametric curve in the N-dimensional space.

[0031] Furthermore, the B-spline parameter curve in the n+1 dimensional space is expressed as: ; The homogeneous coordinate expression of the NURBS parametric curve in N-dimensional space: ;in, represents the point of the NURBS parametric curve at parameter u, is a homogeneous coordinate conversion function, which is used to project weighted coordinates to ordinary coordinates. is the weight of control point i, is the position vector of the ith control point, is the B-spline basis function corresponding to the ith control point, with an order of k, Indicates the value range of parameter u, from 0 to 1 covering the entire curve.

[0032] Specifically, in the construction of NURBS curves, control points and weights are usually separated and represented as independent components of control points and weights. In order to process in a higher dimensional space (i.e., n+1 dimensional space), it is necessary to combine the weights with the control points to form weighted control points. The construction method of weighted control points is to combine the control point di and the weight wi of the corresponding control point to obtain a new weighted control point: Di=[wi,di,wi]. The weighted control point in the n+1 dimensional space contains not only the information of the control point, but also the weight information, so that the influence of the weight on the curve shape can be considered in the subsequent processing. All weighted control points are used to construct the B-spline parametric curve, and a new B-spline parametric curve can be defined in the n+1 dimensional space.

[0033] The general expression of a B-spline curve is as follows: ;in, represents a B-spline parametric curve in n+1 dimensional space, is the B-spline basis function corresponding to the i-th control point, with an order of k, which controls the smooth transition of the curve between each control point. represents the value range of parameter u, covering the entire curve from 0 to 1. Through this formula, the B-spline parametric curve in n+1 dimensional space is obtained by linearly combining weighted control points, which allows the curve to be adjusted accurately not only according to the position of the control points, but also according to the weights.

[0034] In n+1 dimensional space, the calculation of B-spline curve is based on the combination of weighted control points, and the calculation of this combination in high-dimensional space is likely to not conform to the traditional three-dimensional or two-dimensional geometric form. Therefore, in order to convert the B-spline curve into a standard NURBS curve, it is necessary to project it onto the hyperplane of w=1 to obtain the homogeneous coordinate expression of the NURBS parametric curve in N-dimensional space: ;in, represents the point of the NURBS parametric curve at parameter u, It is a homogeneous coordinate transformation function that projects the weighted coordinates into ordinary coordinates. Since the weighted control points are located in a high-dimensional space, the homogeneous coordinate transformation function normalizes them so that the curve can be presented in the ordinary coordinate system, which is then used to define the actual machining path. is the weight of control point i, is the position vector of the ith control point.

[0035] Through this process, the original B-spline curve is combined with the weight information and converted into a homogeneous coordinate form suitable for NURBS, thereby accurately describing the geometric shape of the denture and providing the necessary parameters and paths for CNC machining.

[0036] Further, step 4 of this application includes:

[0037] The recursive algorithm is used to recursively solve the denture contour NURBS parameter curve to obtain the corresponding coordinates of the parameters on the curve and the coordinates of each point; discrete interpolation points are obtained based on the coordinates of each point; the NURBS parameter curve is discretely integrated, and the length of the curve is approximately obtained by accumulating the distances between the discrete interpolation points.

[0038] The formula for the curve length is , where the arc length increment ds is expressed as the rate of change of the curve parameter u, which is divided into the square root of the sum of the squares of the three components x, y, and z. , , They are The derivatives of the x, y, and z components of is the dot product of the derivative vector of the curve and itself.

[0039] Specifically, based on the homogeneous coordinate expression of the NURBS parametric curve in N-dimensional space, the basis function is calculated by a recursive algorithm (such as the De Boer algorithm) The value of , and the control point and weight are substituted into the expression. The coordinate points corresponding to the discretized parameter u value can be solved one by one to obtain the coordinates of each point. By dividing the parameter u from 0 to 1 into several small intervals (for example, the step size is 0.01), the coordinate point C(u) corresponding to each discretized parameter u on the curve is recursively solved, that is, the discrete interpolation points of the curve are obtained. The interpolation points are the key points in the processing path, and the CNC machine tool will generate the processing trajectory based on these interpolation points. In an exemplary experiment, if the parameter u is taken from 0 to 1 with a step size of 0.01, then for a NURBS curve, about 100 interpolation points can be obtained, which represent the discrete positions on the curve in turn. Assume that the coordinates of several of the interpolation points are C(0.01)=(1.0,2.0,1.5), C(0.02)=(1.1,2.1,1.55), etc. These points can accurately describe the shape of the curve. After obtaining the discrete interpolation points, the curve length is approximately calculated by discrete integral. The formula for the curve length is: , where the arc length increment ds is expressed as the rate of change of the curve parameter u, which is divided into the square root of the sum of the squares of the three components x, y, and z. , , They are The derivatives of the x, y, and z components of is the dot product of the derivative vector of the curve and itself. For example, assuming that the distance between adjacent interpolation points C(0.01) and C(0.02) is 0.15 mm, the cumulative value calculated for each subsequent distance segment will eventually approach 10 mm, so that the approximate total length of the curve can be obtained.

[0040] The coordinates of each discrete point on the NURBS parametric curve are obtained through a recursive algorithm, and then the distances between these discrete interpolation points are accumulated using the discrete integration method to approximately calculate the length of the curve, ensuring the accurate representation of the curve and the smoothness of the processing path, thereby improving the accuracy and efficiency of denture processing.

[0041] Further, step five of this application includes:

[0042] Starting from the initial control point sequence, the derivatives of the control points are recursively calculated until the derivative value of the curve at each interpolation point is obtained; the derivative value at each interpolation point is used to construct the tangent vector of the curve at each interpolation point; the first-order derivative vector and the second-order derivative vector of the denture contour NURBS parameter curve are calculated respectively; and the curvature change is calculated through the first-order derivative vector and the second-order derivative vector.

[0043] Specifically, the shape of the denture contour NURBS parameter curve is determined by a series of control points and weights. The initial control point sequence is a sequence of control points in order. Starting from the initial control point sequence, the derivatives of the curve under different parameters are calculated by a recursive algorithm to obtain the derivative values ​​at each interpolation point. These derivative values ​​will be used for the subsequent calculation of the tangent vector. The derivative vector describes the instantaneous direction and speed of the curve at a certain parameter position. The derivative values ​​obtained by recursion can be used to construct the tangent vector of the curve at each interpolation point. For each interpolation point, its tangent vector represents the direction of the curve at that point. The calculation result of the tangent vector can help determine the direction of the machining path. In actual machining, the tangent vector can be used to control the feed direction of the tool to make the machining path smoother. The first-order derivative vector represents the tangent direction and speed of the curve, and the tangent vector can be used as the first-order derivative vector. The second-order derivative vector represents the acceleration direction of the curve, that is, the rate of change of the tangent vector. The size of the second-order derivative reflects the curvature of the curve. On the machining path, the second-order derivative can be used to detect the sharp turning position of the curve so as to decelerate in these areas.

[0044] Curvature is a measure of the degree of curvature of a curve at a certain point. It depends on the first and second derivatives of the curve at that point. First, the modulus of the cross product of the first-order derivative vector and the second-order derivative vector is calculated, and then divided by the cube of the modulus of the first-order derivative vector. The result is the curvature, from which the curvature at different interpolation points can be obtained, thereby forming a curvature change. The curvature at different interpolation points reflects the curvature change of the curve. In the machining path planning, the density of the interpolation points and the feed speed of the tool can be adjusted according to the curvature value. By recursively calculating the derivatives of the control points, the tangent vector of the curve at each interpolation point is obtained, and then the curvature change is calculated using the first-order derivative and the second-order derivative, and the precise path information of the curve can be obtained. This information is very important in CNC machining, especially in the machining of complex shapes such as dentures, which helps to optimize the path, control the feed speed, and improve the machining accuracy and surface quality.

[0045] Furthermore, step six of this application includes:

[0046] According to the curvature change determined by the derivative vector, the interpolation point density is identified, and the interpolation point density is proportional to the curvature change. When the curvature change is large, the interpolation point density is large, and when the curvature change is small, the interpolation point density is small; the curve length is divided into curves, and the length of each curve division is a preset step length; according to the interpolation point density, the interpolation point position of the curve division length is identified to obtain the interpolation point coordinates, and the interpolation point parameters are identified based on the interpolation point coordinates; based on the interpolation point coordinates and the interpolation point parameters, path connection is performed to obtain a processing path.

[0047] Specifically, first, based on the change in curvature, the density of interpolation points can be dynamically adjusted. Interpolation points are a series of discrete points on the CNC machining path. The tool will pass through these points in sequence to form a machining path. In order to ensure the accuracy and machining quality of the path, the density of interpolation points is proportional to the change in curvature: when the curvature changes greatly (sharp turns), the density of interpolation points increases to ensure smooth transition of the tool along the curve. When the curvature changes slightly (flat parts), the density of interpolation points decreases to reduce unnecessary calculations. For example, assume that the curvature of the curve at different interpolation points changes as follows: at u=0.2, the curvature = 0.45, and the density of interpolation points is 10 points / unit length. At u=0.5, the curvature = 0.2, and the density of interpolation points is 5 points / unit length. At u=0.8, the curvature = 0.05, and the density of interpolation points is 2 points / unit length. This density adjustment ensures that more interpolation points are inserted in the sharp turn area to improve machining accuracy, while the number of interpolation points is reduced in the flat area to improve efficiency.

[0048] The length of the curve is calculated by numerical integration. In order to further determine the position of the interpolation point, the curve is divided into several segments, and the length of each segment is a preset step length. The main purpose of dividing the curve is to provide a uniform segment length in the processing path, which is convenient for the uniform distribution of the interpolation points. In the high curvature area, the segment length can be reduced to make the interpolation points more densely distributed to ensure the smoothness and accuracy of the tool movement. Then, the interpolation point position is determined by dividing the length of each curve segment according to the interpolation point density, that is, the interpolation points are distributed within the length of each curve segment according to the interpolation point density, thereby obtaining the interpolation point coordinates. For each interpolation point, its position is calculated using the homogeneous coordinate expression of the NURBS curve.

[0049] After obtaining the interpolation point coordinates, it is also necessary to identify the processing parameters of each interpolation point (such as feed rate, cutting depth, etc.). These parameters can be dynamically adjusted based on curvature, curve segment length and processing requirements. In high curvature areas, the feed rate is appropriately reduced to improve processing accuracy; in low curvature areas, the feed rate is increased to improve processing efficiency. For example, in sharp turning areas, the interpolation point parameters are lower feed rates (such as 10mm / min); and in flat areas, the feed rate can be increased to 50mm / min. The specific settings can be made by professional and technical personnel in this field based on actual experience. Finally, all interpolation points are connected in sequence, and the interpolation point coordinates and processing parameters will be integrated into NC codes (such as G codes) to control the machine tool tool to move along the trajectory of these interpolation points. The NC code includes information such as the coordinates, feed rate and cutting depth of each interpolation point. By dynamically adjusting the density of interpolation points through curvature changes, precise control of the processing path is achieved, which not only ensures high-precision processing of complex surfaces, but also optimizes processing efficiency, enabling CNC machine tools to perform path control more effectively.

[0050] Furthermore, the present application also includes the following steps:

[0051] According to the interpolation point parameters and interpolation point coordinates, the target accuracy, denture performance requirements, and processing parameters are extracted; the curvature change of the interpolation point coordinates is obtained; according to the target accuracy, denture performance requirements, and processing parameters, the accuracy constraint parameters are obtained; the curvature spacing is adaptively adjusted according to the curvature change and the accuracy constraint parameters, and a smooth transition adjustment strategy is determined, wherein the smooth transition adjustment strategy is to insert smooth transition points into intervals with high curvature changes and high precision constraints; based on the smooth transition adjustment strategy, the interpolation point coordinates are inserted and adjusted, and smoothly connected to obtain the processing path.

[0052] Specifically, in denture processing, target accuracy and denture performance requirements are core considerations. Target accuracy refers to the error range of the final processing path, which is usually determined by the complexity of the surface and the processing requirements. Assuming that the target accuracy requirement is controlled within ±0.01mm, the denture surface requires high finish, and the surface roughness needs to be less than 0.8μm, the smoothness and density of the path need to be improved in the complex surface area to meet the processing requirements. Denture performance requirements include indicators such as the strength and surface finish of the denture, which will directly affect the processing path planning. Processing parameters refer to the interpolation point parameters corresponding to the interpolation point coordinates. In order to ensure that the path is smooth and accurate, it is necessary to calculate the curvature change of the interpolation point coordinates. Curvature refers to the degree of curvature of a point on the curve. The larger the curvature value, the more severe the curvature of the curve near the point. The curvature calculation method has been recorded above and will not be repeated here.

[0053] Based on the target accuracy, denture performance requirements and processing parameters, the accuracy constraint parameters in the path planning can be determined. These parameters will be used to adjust the density and distribution of the interpolation points to ensure that the processing path meets the final accuracy and surface requirements. The accuracy constraint parameters can be the requirements for the contact surface or fine edge of the denture, such as requiring the deviation to be less than 0.01mm, which is specifically set by professional and technical personnel in this field based on actual experience.

[0054] According to the curvature change and precision constraint parameters, the curvature spacing is adaptively adjusted. Adaptive adjustment means dynamically adjusting the distribution density of interpolation points according to the curvature change and precision constraint parameters. Specifically, according to the curvature size, the spacing between interpolation points is automatically adjusted. In the high curvature area, the spacing is reduced to increase the density of interpolation points; in the low curvature area, the spacing is expanded to reduce the number of interpolation points, which is used as a smooth transition adjustment strategy. In areas with high curvature and high precision requirements, smooth transition points are inserted to ensure smooth transition of the path at sharp turns to avoid processing errors caused by sudden changes.

[0055] Assuming that the curvature of the curve changes dramatically in the interval from u=0.4 to u=0.5, and this interval belongs to the high-precision area, more transition points will be automatically inserted in this area to reduce the interpolation point spacing to 50% of the original spacing. Finally, the interpolation points are inserted and adjusted based on the smooth transition adjustment strategy, and a continuous machining path is generated through smooth connection, so that the tool can move smoothly along the curve trajectory. The machining path is output through NC code (such as G code), which contains the coordinates, feed speed and other machining parameters of each interpolation point, controls the CNC machine tool to perform precise machining along the path, improves the smoothness and precision of the machining path, and is particularly suitable for high-quality machining of complex denture shapes.

[0056] In summary, the five-axis CNC machining trajectory interpolation method provided by the present application has the following technical effects:

[0057] The target structure information of the denture is collected to extract the denture processing contour; based on the denture processing contour, the curve fitting is performed through the NURBS parameter curve to obtain the denture contour NURBS parameter curve; the denture contour NURBS parameter curve is represented by the alignment coordinates, and the homogeneous coordinate expression of the NURBS parameter curve in N-dimensional space is derived; according to the homogeneous coordinate expression, the coordinates of each point on the denture contour NURBS parameter curve are obtained, and the curve length is calculated using the numerical analysis algorithm; for the denture contour NURBS parameter curve, the derivative vector on the curve is calculated to determine the curvature change of the curve at the interpolation point; according to the curve length and the derivative vector, the interpolation point coordinates are located, and the processing path planning is performed using the interpolation point coordinates. By locating the interpolation point based on the derivative vector and curvature change of the NURBS curve, the density of the interpolation point is dynamically adjusted, and the processing path planning is performed. The processing path finally generated can ensure that the tool moves smoothly along the denture contour, thereby improving the processing quality, significantly reducing the processing time and cost, and meeting the technical effect of high precision and high efficiency requirements of denture manufacturing.

[0058] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present application. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present application. Therefore, the present application will not be limited to the embodiments shown herein, but will conform to the widest scope consistent with the principles and novel features disclosed herein.

[0059] Obviously, those skilled in the art can make various changes and modifications to the present application without departing from the spirit and scope of the present application. Thus, if these modifications and variations of the present application belong to the scope of the present application and its equivalent technology, the present application is also intended to include these modifications and variations.

Claims

1. A five-axis CNC machining trajectory interpolation method, characterized in that: The five-axis CNC machining trajectory interpolation method comprises: Collect the target structure information of the denture and extract the denture processing contour; Based on the denture processing contour, curve fitting is performed through a NURBS parameter curve to obtain a denture contour NURBS parameter curve; Using alignment coordinates to represent the denture contour NURBS parameter curve, and deriving a homogeneous coordinate expression of the NURBS parameter curve in N-dimensional space; According to the homogeneous coordinate expression, the coordinates of each point on the NURBS parameter curve of the denture contour are obtained, and the length of the curve is calculated using a numerical analysis algorithm; For the denture contour NURBS parameter curve, calculating the derivative vector on the curve to determine the curvature change of the curve at the interpolation point; The interpolation point coordinates are located according to the curve length and the derivative vector, and the processing path is planned using the interpolation point coordinates.

2. The five-axis CNC machining trajectory interpolation method according to claim 1, characterized in that: Export the homogeneous coordinate expressions of NURBS parametric curves in N-dimensional space, including: Combine the control point di and the corresponding control point weight wi to obtain the weighted control point: Di=[wi,di,wi]; Using the weighted control points, a B-spline parametric curve in n+1 dimensional space is obtained; The B-spline parametric curve in the n+1 dimensional space is projected onto a hyperplane with w=1 to obtain a homogeneous coordinate expression of the NURBS parametric curve in the N dimensional space.

3. The five-axis CNC machining trajectory interpolation method according to claim 2, characterized in that: The B-spline parametric curve in the n+1 dimensional space is expressed as: ; The homogeneous coordinate expression of the N-dimensional space NURBS parametric curve is: ; in, represents the point of the NURBS parametric curve at parameter u, is a homogeneous coordinate conversion function, which is used to project weighted coordinates to ordinary coordinates. is the weight of control point i, is the position vector of the ith control point, is the B-spline basis function corresponding to the ith control point, with an order of k, Indicates the value range of parameter u, from 0 to 1 covering the entire curve.

4. The five-axis CNC machining trajectory interpolation method according to claim 2, characterized in that: Obtaining the coordinates of each point on the NURBS parameter curve of the denture contour and calculating the length of the curve using a numerical analysis algorithm includes: The recursive algorithm is used to recursively solve the NURBS parameter curve of the denture contour, and the corresponding coordinates of the parameters on the curve are obtained to obtain the coordinates of each point; Obtaining discrete interpolation points according to the coordinates of each point; Discrete integration is performed on the NURBS parameter curve, and the length of the curve is approximately obtained by accumulating the distances between the discrete interpolation points.

5. The five-axis CNC machining trajectory interpolation method according to claim 4, characterized in that: The formula for the curve length is , where the arc length increment ds is expressed as the rate of change of the curve parameter u, which is divided into the square root of the sum of the squares of the three components x, y, and z. , , They are The derivatives of the x, y, and z components of is the dot product of the derivative vector of the curve and itself.

6. The five-axis CNC machining trajectory interpolation method according to claim 1, characterized in that: For the denture contour NURBS parameter curve, a derivative vector on the curve is calculated to determine the curvature change of the curve at the interpolation point, including: Starting from the initial control point sequence, the derivatives of the control points are recursively calculated until the derivative value of the curve at each interpolation point is obtained; The derivative value at each interpolation point is used to construct the tangent vector of the curve at each interpolation point; respectively calculating the first-order derivative vector and the second-order derivative vector of the denture contour NURBS parameter curve; The curvature change is calculated using the first-order derivative vector and the second-order derivative vector.

7. The five-axis CNC machining trajectory interpolation method according to claim 6, characterized in that: Locating interpolation point coordinates according to the curve length and the derivative vector, and using the interpolation point coordinates to plan a machining path, including: According to the curvature change determined by the derivative vector, the interpolation point density is identified, wherein the interpolation point density is proportional to the curvature change, and when the curvature change is large, the interpolation point density is large, and when the curvature change is small, the interpolation point density is small; Divide the length of the curve into curves, and divide each curve into sections with a preset step length; Identify interpolation point positions for the curve division length according to the interpolation point density, obtain the interpolation point coordinates, and identify interpolation point parameters based on the interpolation point coordinates; Based on the interpolation point coordinates and the interpolation point parameters, path connection is performed to obtain a processing path.

8. The five-axis CNC machining trajectory interpolation method according to claim 7, characterized in that: Based on the interpolation point coordinates and the interpolation point parameters, path connection is performed to obtain a processing path, including: Extracting target accuracy, denture performance requirements, and processing parameters based on the interpolation point parameters and interpolation point coordinates; Obtaining a curvature change of the interpolation point coordinates; Obtaining precision constraint parameters according to the target precision, denture performance requirements, and processing parameters; Adaptively adjust the curvature spacing according to the curvature change and the precision constraint parameter, and determine a smooth transition adjustment strategy, wherein the smooth transition adjustment strategy is to insert smooth transition points into intervals with high curvature changes and high precision constraints; The interpolation point coordinates are inserted and adjusted based on the smooth transition adjustment strategy, and smoothly connected to obtain the processing path.

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