A spiral trajectory smoothing compression method for implant CNC machining

Abstract

The present invention relates to a spiral trajectory smoothing and compression method for CNC machining of implants. This method, which belongs to the field of CNC machining, is used to address the problem that the tool trajectories of parts such as implants are mostly circular arcs and spatial spirals, which are then discretized into a series of small line segments after being processed by CAM (Computer Aided Manufacturing) software. Based on the process characteristics of the implant workpiece, the method of the present invention first fits the tool trajectory described by the small line segments in a two-dimensional plane, then performs spatial fitting in the Z direction, and classifies and fits various curves. This geometrically improves the smoothness of the machining trajectory, thereby enhancing the speed stability during the machining process, improving surface machining quality, and shortening machining time.

Description

Technical Field

[0001] The present disclosure relates to the field of numerical control machining, and in particular to a spiral trajectory smoothing and compressing method for numerical control machining of implants. Background Art

[0002] In the CNC machining of complex parts such as dental implants, the tool paths generated by computer-aided manufacturing software are mostly composed of continuous small line segments, such as Figure 1 shown.

[0003] In the prior art, methods for smoothing tool trajectories for small line segments can be divided into two main categories: local smoothing and global smoothing algorithms. Local trajectory smoothing techniques primarily insert transition curves, such as broken lines, arcs, and parametric curves, at the corners of adjacent tiny straight line segments to smooth the CNC machining trajectory and increase the speed at which the moving parts of the CNC machine tool pass through corners, thereby improving machining speed and quality. Prior art document 1, "Xiao QB, Wan M, Liu Y, et al. Space cornersmoothing of CNC machine tools through developing 3D general clothoid [J]. Robotics and Computer-Integrated Manufacturing, 2020, 64: 101949," uses 3D clothoid curves to achieve smooth transitions at spatial corners, effectively improving machining quality and efficiency. Global smoothing algorithms fit discrete command points into a smooth machining path through interpolation or approximation. For example, in the literature 2, "Bi QZ, Huang J, Lu YA, et al. A general, fast and robust B-spline fitting scheme for micro-linetool path under chord error constraint [J]. Science China Technological Sciences, 2019, 62(2): 321-332.", a B-spline fitting method under chord error constraint is proposed. This method significantly reduces the amount of calculation and improves the processing efficiency of small line segment trajectories under the premise of strictly constraining the chord height error.

[0004] As can be seen from the above, when the small segment smoothing technology is used for smooth transition or global fitting, the CNC system needs to have the interpolation function of the corresponding curve, which places high demands on the control system. The mechanical vibration caused by frequent acceleration and deceleration under the small segment trajectory also affects the quality of part processing. Existing research mainly considers general CNC systems, but in actual use, most of the functions of general systems are not used when processing parts such as abutments and implants, resulting in waste and increased equipment costs. Since the tool trajectories of parts such as abutments and implants in oral implants are mostly arcs and spatial spirals, it is of great significance to develop a dedicated spiral trajectory smoothing compression method for dental implant-specific CNC systems. Summary of the Invention

[0005] In response to the above-mentioned existing technologies, the present invention proposes a spiral trajectory smoothing and compression method for CNC machining of implants. Under the premise of meeting the accuracy, the tool trajectory of each part of the implant is smoothly compressed to improve the speed stability during the machining process, improve the surface machining quality, and shorten the machining time.

[0006] The technical solutions of the present invention are as follows:

[0007] A spiral trajectory smoothing and compression method for CNC machining of implants uses corresponding curves to smoothly compress different tool trajectory models based on the process characteristics of the implant workpiece, facilitating subsequent trajectory interpolation. Specifically, the tool trajectory described by small line segments is first fitted in a two-dimensional plane, then spatially fitted in the Z direction. Various curves are classified and fitted, geometrically improving the smoothness of the machining trajectory to enhance the speed stability during machining, improve surface machining quality, and shorten machining time. The method comprises the following steps:

[0008] S100, based on the machining coordinate system, obtaining continuous G1 data points of the implant tool trajectory, and obtaining a projection point set of these data points on the XY projection plane;

[0009] Take the last point of the projection point set as the first tail point, and start from the first point of the projection point set to obtain a set of projection points as the current projection point set;

[0010] S200, performing plane fitting based on the current projection point set until a plane fitting breakpoint or the first tail point is encountered, thereby obtaining a plane curve;

[0011] S300: If the plane curve is a projection of a spatial spiral curve on an XY projection plane, performing spatial spiral curve fitting on the plane curve;

[0012] S400. If the end point of the plane curve is not the first end point, the plane fitting breakpoint is used as the starting point, the next set of projection points is obtained as the current projection point set, and S200 is re-entered for plane fitting; otherwise, the fitted curve is converted into NC (Numerical Control) code that can be recognized by the numerical control system.

[0013] As a further improvement of the previous technical solution, the plane fitting is performed based on the current projection point set, and straight line segments and arc segments are distinguished in the plane fitting, so as to convert the tool path described by small line segments into large straight line segments and arc segments. This can reduce the amount of data and improve the overall processing efficiency and processing quality. Specifically, the steps include:

[0014] Step marked S: Using the current set of projected points, use the Pratty fitting method to determine the parameters of the following circle:

[0015] A, B, C, and D are the circle parameters to be determined;

[0016] If A=0, the points in the current projection point set are collinear;

[0017] If the last point of the current projection point set is not the first last point, take the last point as the first point, get the next projection point set as the current projection point set, and return to the step marked S;

[0018] If A≠0, calculate the arc fitting error of the current projection point set;

[0019] If the fitting error meets the first set threshold and the tail point of the current projection point set is not the first tail point, then trace back one point as the new tail point and add it to the current projection point set, and return to the step marked S;

[0020] If the fitting error does not meet the first set threshold, the plane fitting is terminated by retracing one point as a breakpoint.

[0021] In the above technical solution, an implementation method of determining the parameters of the following circle using the current projection point set and the Pratty fitting method includes the following steps:

[0022] The first point of the current projection point set is recorded as (x1, y1), and the last point is recorded as (x n ,y n ), we get the following start and end point constraints:

[0023] A, B, C, and D are the circle parameters to be determined;

[0024] Thus we get:

[0025] m1, n1, m2, n2 are constants;

[0026] According to the Pratty arc fitting method, the target equation is established as:

[0027]

[0028] Bringing in the constraints of the first and last points, the above objective equation is transformed into Under constraint B 2 +C 2 -4AD = 1, where:

[0029] s i =x i +n1y i +n w , i=1,2,…,n;

[0030] The Lagrange multiplier method is used to solve the above minimum problem. The Lagrange multiplier is denoted as μ, and we get:

[0031] G(U,μ)=U T MU-μ(U T VU-1)

[0032] in:

[0033] Constraints: U T VU=1, where:

[0034] The value of matrix U is the corresponding matrix V -1 The eigenvector of the smallest non-negative eigenvalue of M is used to obtain the values of the circle's parameters A, B, C, and D.

[0035] In the above technical solution, one implementation method of calculating the arc fitting error of the current projection point set includes the following steps:

[0036] Calculate the radius R and center coordinates of the circle from the circle parameters;

[0037] Calculate the distance from the first projection point to each point of the breakpoint to the center of the circle in turn, and record it as , i represents the identifier of the current projection point being calculated;

[0038] Calculate the arc fitting error at the current projection point

[0039] In the above technical solution, one implementation method of spatial spiral curve fitting includes the following steps:

[0040] Step marked P: Calculate the helix parameters based on the Z-axis coordinates of the current starting and ending points:

[0041]

[0042] Among them, Z s is the starting point of the arc, Z e is the end point of the arc, θ se is the central angle of the arc;

[0043] For each data point in this curve, use i to represent the current projection point identifier and calculate the Z-axis fitting error δ of the spiral line. z :

[0044] δ z =|Z s +ρθ i -Z i |

[0045] Where: Z i is the Z coordinate of the current projection point, θ i The center angle of the arc formed by the current projection point and the previous data point;

[0046] The plane curve fitting error is denoted as δ c , calculate the spatial fitting error δ of the helix h :

[0047]

[0048] Determine the spatial fitting error δ h whether a second set threshold is met;

[0049] If it is satisfied, a cylindrical helix is obtained. Otherwise, the point with the maximum error is set as the breakpoint, the next point of the breakpoint is obtained as the first point, the current first and last points are updated, and the process returns to the step marked as P.

[0050] One implementation method of calculating the central angle is to use an incremental form:

[0051] θ se =∑θ i

[0052] Where: θ i is the angle between two adjacent data points.

[0053] In the above technical solution, simple arcs and spatial spirals are used to fit small segment tool trajectories. Compared with most local transition smoothing methods, this method avoids the problem of difficulty in speed planning when processing tiny segments. Compared with the global smoothing of spline curves, this method is more specialized, and the CNC system does not require complex spline interpolation functions, which has a higher cost-effectiveness. In addition, this method can smoothly compress different tool trajectory models into corresponding spline curves for trajectory interpolation, which has better processing effects. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0055] Figure 1 , tool path generation process diagram;

[0056] Figure 2 , schematic diagram of arc fitting error calculation;

[0057] Figure 3 , schematic diagram of fitting effect;

[0058] Figure 4 , schematic diagram of error limitation effect. DETAILED DESCRIPTION

[0059] The technical solutions in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments.

[0060] In dental implants, tool paths for components like abutments and implants are often arcs and spirals. However, after processing using CAM (Computer Aided Manufacturing) software, these paths are discretized into a series of small line segments. The method presented in this paper processes these tool paths, achieving high-speed, high-precision machining of implant components through smooth compression of these discrete small line segments.

[0061] One embodiment of the method of the present invention is applied to the processing of dental implants, and the steps in the processing flow can be executed out of sequence. On the contrary, some steps can be implemented in reverse order or simultaneously. In addition, one or more other steps can be added to the process. One or more steps can be removed from the process. The method of the present invention is preferably implemented in a processing coordinate system, but a coordinate system can also be established by itself. By fitting twice in the XY plane and the Z direction, straight lines, circular arcs and spatial spirals are distinguished and fitted to achieve global smoothing of small segment tool trajectories, so that when forward speed planning is performed between each curve segment later, the smoothness of the overall speed can be guaranteed, thereby achieving efficient and high-quality processing of implants. Specifically comprising the following steps:

[0062] S100, in one process, obtaining continuous G1 data points P of the implant tool trajectory in the machining coordinate system i , i = 1, 2, 3, ... n, and obtain the projection point set of these consecutive data points on the XY projection plane. The last point of the projection point set is used as the first tail point. Starting from the first projection point, the first reading of at least 3 data points is used as the current data point set.

[0063] S200 , performing plane fitting based on the current projection point set until a plane fitting breakpoint or the first tail point is encountered, thereby obtaining a plane curve.

[0064] The plane fitting based on the current projection point set includes the following steps:

[0065] S201. Establish the equation of the circle as follows:

[0066] A, B, C, and D are the circle parameters to be determined.

[0067] S202: Using the current data point set, determine the parameters A, B, C, and D of the circle using the Pratty fitting method.

[0068] In the Pratty fitting method, the arc fitting calculation is performed using the first and last point constraints. Specifically:

[0069] S2021, record the first point of the current data point set as (x1, y1), and the last point as (x n ,y n ), the first and last point constraints can be expressed as:

[0070]

[0071] S2022. Express parameters C and D using A and B. For convenience, replace the coefficients of A and B with the coordinates of the first and last points in each expression with constant parameters m1, n1, m2, and n2, resulting in the following simplified expression:

[0072] m1, n1, m2, n2 are constants;

[0073] S2023. According to the Pratty arc fitting method, the target equation is established as:

[0074]

[0075] S2024, bring in the first and last point constraints, and transform the above equation into Under constraint B 2 +C 2 -4AD=1 is the minimum value.

[0076] Will Written in matrix form: G = U T MU, where:

[0077]

[0078] s i =x i +n1y i +n2;

[0079] The constraints can be written in matrix form as:

[0080] U T VU=1, where:

[0081] S2025. Use the Lagrange multiplier method to solve the minimum problem. Let the Lagrange multiplier be μ, and we get:

[0082] G(U,μ)=U T MU-μ(U T VU-1)

[0083] S2026, Therefore, the value of the matrix U is the corresponding matrix V -1 The value of the eigenvector of the smallest non-negative eigenvalue of M is obtained, thereby obtaining the values of the circle parameters A, B, C, and D.

[0084] At this point, the arc parameters can be obtained: Center coordinates: and radius

[0085] S203. According to the parameter A of the circle, the type of the plane curve fitted by the current projection point set can be obtained.

[0086] S2031. If A = 0, the fitting result is a straight line. If the first tail point is encountered, execute S500; otherwise, take the tail point of the current projection point set as the first point, obtain the next set of projection points as the current projection point set, and return to S200;

[0087] S2032: If A≠0, the fitting result is a plane arc. In this case, it is necessary to determine whether to end the plane fitting based on the fitting error of the current plane arc.

[0088] One implementation method of the current plane arc fitting error is as follows Figure 2 As shown, the following steps are included:

[0089] S20321. Calculate the radius R and center coordinates of the circle based on the circle parameters;

[0090] S20322. Calculate the distance from the first projection point to each point of the breakpoint to the center of the circle, and record it as i represents the identifier of the current projection point being calculated;

[0091] S20323, calculate the fitting error of the current plane arc

[0092] If the fitting error of the current plane arc meets the first set threshold, then trace back one point as the new end point of the current projection point set, and return to S200 to fit a new arc. The arc has one more point than the original arc.

[0093] If the fitting error of the current plane arc does not meet the first threshold setting requirement, the process moves back one point as a breakpoint of the current plane arc, and then executes S300 .

[0094] S300: Determine whether the current plane arc is a projection of a spatial spiral curve on an XY projection plane based on the Z-axis coordinates of the first and last points of the current plane arc;

[0095] S301. If the current plane arc is the projection of a spatial spiral curve on the XY projection plane, calculate the spiral parameters according to the Z-axis coordinates of the first and last points of the current plane arc:

[0096]

[0097] Among them, Z s is the starting point of the current plane arc, Z e is the end point of the current plane arc, θ se The central angle of the current plane arc is calculated in the form of increments. se =∑θ i , that is, the accumulation of the central angles of two adjacent points, avoiding the range limitation when calculating the angle using the arc cosine.

[0098] S302, calculating the spatial fitting error of the spatial spiral curve:

[0099]

[0100] Where: z is the Z-axis fitting error of the spatial spiral curve, δ z =|Z s +ρθ i -Z i |, Z i is the Z coordinate of the current data point, θ i It is the central angle of the plane arc formed by the current projection point and the previous projection point, that is, the angle between two adjacent projection points.

[0101] S303: If the calculated spatial fitting error meets the second set threshold, a fitted spatial spiral curve is obtained;

[0102] S304. If the calculated spatial fitting error does not meet the second set threshold requirement, the point with the largest spatial fitting error is set as the current spatial fitting breakpoint, and it is determined whether the current spatial fitting is completed; if the spatial fitting is not completed, the current spatial fitting breakpoint is used as the new starting point, and the spatial fitting is continued until the spatial fitting reaches the data point corresponding to the end point of the current plane arc.

[0103] S400. When the arc is not the projection of the spatial spiral curve on the XY projection plane, or when the spatial fitting is completed, if the end point of the plane curve is not the first end point, the plane fitting breakpoint is used as the first point, the next set of projection points is obtained as the current projection point set, and S200 is re-entered for plane fitting; if the end point of the plane curve is the first end point, S500 is entered.

[0104] S500: Convert the fitted curve into NC (Numerical Control) code that can be recognized by a numerical control system.

[0105] S600, import NC code into CNC system and use forward speed planning for CNC machining.

[0106] Figure 3 The figure shows the effect of smooth compression of a certain section of the dental implant processing trajectory (3378 tool positions) under a given error limit of 5 microns. The hollow points are the breakpoints of the fitting curve. The number of arc segments and spiral segments obtained by compression is 8, and the compression ratio is 47.6:1. Figure 4 The error limitation effect of each point verifies the effectiveness of the spiral trajectory smoothing compression method proposed in this invention.

[0107] Through the above description of the embodiments, those skilled in the art will clearly understand that the present disclosure can be implemented using software plus necessary general-purpose hardware. Of course, it can also be implemented using dedicated hardware, including application-specific integrated circuits, dedicated CPUs, dedicated memories, and dedicated components. Generally speaking, any function performed by a computer program can be easily implemented using corresponding hardware. Moreover, the specific hardware structures used to implement the same function can also be diverse, such as analog circuits, digital circuits, or dedicated circuits. However, for the present disclosure, software implementation is often the preferred embodiment.

[0108] Although the embodiments of the present invention have been described above with reference to the accompanying drawings, the present invention is not limited to the above-mentioned specific embodiments and application fields. The above-mentioned specific embodiments are merely illustrative and instructive, and are not restrictive. A person skilled in the art, guided by this specification and without departing from the scope of protection of the claims of the present invention, may also devise various forms, all of which fall within the scope of protection of the present invention.

Claims

1. A spiral trajectory smoothing compression method for implant CNC machining, characterized in that: The method comprises the following steps: S100, based on the machining coordinate system, obtaining continuous G1 data points of the implant tool trajectory, and obtaining a projection point set of these data points on the XY projection plane; Take the last point of the projected point set as the first tail point, and start from the first point of the projected point set to obtain at least 3 data points as the current projected point set; S200, performing plane fitting based on the current projection point set until a plane fitting breakpoint or the first tail point is encountered, thereby obtaining a plane curve; S300: If the plane curve is a plane circular arc, determine whether it is a projection of a spatial spiral curve on an XY projection plane based on the Z-axis coordinates of the first and last points of the plane circular arc. If the plane arc is the projection of the spatial spiral curve on the XY projection plane, the plane arc is subjected to spatial spiral curve fitting, and the steps include: Calculate the spiral parameters: , is the starting point of the plane arc, is the end point of the plane arc, is the central angle of the plane arc, , Projection point The central angle of the plane arc formed with the previous projection point; Calculate the spatial fitting error of the spatial spiral curve: , is the Z-axis fitting error of the spatial spiral curve, , is the Z coordinate of the data point corresponding to the projection point i, is the fitting error of the arc at the projection point i; If the calculated spatial fitting error meets the second set threshold requirement, a well-fitted spatial spiral curve is obtained; If the calculated spatial fitting error does not meet the second set threshold requirement, the point with the largest spatial fitting error is set as the current spatial fitting breakpoint, and it is determined whether the current spatial fitting is completed; if the spatial fitting is not completed, the current spatial fitting breakpoint is used as the new starting point, and the spatial fitting is continued until the spatial fitting reaches the data point corresponding to the end point of the current plane arc; S400: When the arc is not the projection of the spatial spiral curve on the XY projection plane, or when the spatial fitting is completed, if the end point of the plane arc is not the first end point, the plane fitting breakpoint is used as the starting point, the next set of projection points is obtained as the current projection point set, and the process of S200 is re-entered for plane fitting; otherwise, S500 is executed; S500: Convert the fitted curve into NC code that can be recognized by the numerical control system.

2. The method according to claim 1, characterized in that The plane fitting based on the current projection point set includes the following steps: Step marked S: Using the current set of projected points, use the Pratty fitting method to determine the parameters of the following circle: , A, B, C, D are the circle parameters to be determined; If A=0, then the points in the current projection point set are collinear; If the last point of the current projection point set is not the first last point, take the last point as the first point, get the next projection point set as the current projection point set, and return to the step marked S; If A≠0, calculate the arc fitting error of the current projection point set; If the fitting error meets the first set threshold and the tail point of the current projection point set is not the first tail point, then trace back one point as the new tail point and add it to the current projection point set, and return to the step marked S; If the fitting error does not meet the first set threshold, the plane fitting is terminated by retracing one point as a breakpoint.

3. The method according to claim 2, characterized in that The method of using the current projection point set and the Pratty fitting method to determine the parameters of the following circle includes the following steps: The first point of the current projection point set is recorded as , the last dot is recorded as , we get the following start and end point constraints: , A, B, C, D are the circle parameters to be determined; Thus we get: , 、 、 、 is a constant; According to the Pratty arc fitting method, the target equation is established as: Bringing in the constraints of the first and last points, the above objective equation is transformed into Under the constraints The minimum value under , where: ， ， ； The Lagrange multiplier method is used to solve the above minimum problem, and the Lagrange multiplier is denoted as ,get: in: , Constraints: ,in: ; matrix The value of is the corresponding matrix The eigenvector of the smallest non-negative eigenvalue is used to obtain the values of the circle's parameters A, B, C, and D.

4. The method according to claim 2, characterized in that The calculation of the arc fitting error of the current projection point set includes the following steps: Calculate the radius of a circle from its parameters , circle center coordinates; Calculate the distance from the first projection point to each point of the breakpoint to the center of the circle in turn, and record it as , Indicates the current projection point identifier of the calculation; Calculate the arc fitting error at the current projection point .

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