Sawing method and system of high-speed circular sawing machine based on least square method

Abstract

The invention relates to a high-speed circular sawing machine sawing method and system based on a least square method, and the method comprises the following steps: S1, collecting the non-uniform point cloud data of the edge of a workpiece through a laser scanner, and generating a workpiece edge discrete sampling point set containing N three-dimensional coordinate points; s2, performing segmented cubic spline interpolation processing on the discrete sampling point set to generate a continuous and derivable cutting reference curve; s3, a mathematical model with the sum of squares of the notch track errors as a target function is constructed, the saw blade rotating speed n, the feeding speed v and the sawing depth d serve as optimization variables of the model, and sawing force F is introduced to serve as a constraint condition; s4, on the basis of the mathematical model and the cutting reference curve, the saw blade rotating speed n, the feeding speed v and the sawing depth d are adjusted through an iterative algorithm, the sum of squares of cut track errors is converged under the condition that the constraint condition of sawing force F is met, and an optimal technological parameter combination (n, v and d *) is obtained; and S5, controlling the saw cutting blade to work according to the optimal process parameter combination.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of robot control, in particular to a high-speed circular saw machine sawing method based on least squares. BACKGROUND

[0002] In modern manufacturing, high-speed circular saw machines are widely used in the processing of metals, wood, plastics and other materials as a high-efficiency cutting equipment. The core goal is to achieve high-speed and low-loss continuous production while ensuring cutting accuracy. However, traditional high-speed circular saw machine sawing methods have many technical bottlenecks and cannot meet the increasing industrial demand.

[0003] Traditional processes usually rely on manual measurement or simple sensors to obtain workpiece profile information, resulting in uneven distribution and insufficient density of discrete sampling points. This rough data processing method cannot accurately reflect the characteristics of complex curved surfaces, especially when dealing with irregular shapes, which can easily produce large fitting errors. For example, using the method of approximating curves with straight lines can introduce significant shape distortion, directly affecting the accuracy of subsequent cutting path planning.

[0004] A method and device for measuring the transverse vibration of a diamond wire saw are disclosed in Chinese patent CN115082397A. A given vibration excitation signal is applied to the two support ends of the diamond wire saw on the vibration measurement bench by a vibration exciter. Industrial cameras are used to capture images at each time during the transverse vibration of the diamond wire saw. The collected images are preprocessed and traversed to obtain pixel information. The inner diameter boundary and center coordinates of the wire saw are obtained by multiple least squares linear fitting. Finally, the transverse vibration displacement curve of the diamond wire saw is obtained. Although the above-mentioned scheme uses an industrial camera to capture images and performs multiple least squares linear fitting to obtain the relevant parameters of the diamond wire saw by applying a vibration excitation signal with a vibration exciter, the principle of this method is based on linear approximation under static or quasi-static conditions. The interaction between the saw blade and the workpiece in the actual operation of the high-speed circular saw machine is a highly nonlinear process. It is difficult to track the instantaneous deformation state of the saw blade during high-speed rotation in real time by relying solely on linear fitting, thus establishing an accurate dynamic model.

[0005] Therefore, we propose a high-speed circular saw machine sawing method and system based on least squares.

[0006] The above content is only used to assist in understanding the technical solutions of the present application and does not represent the acknowledgement of the above content as prior art. SUMMARY

[0007] The present application proposes a high-speed circular saw machine sawing method and system based on least squares, aiming to solve the problem that the traditional static calibration method in the prior art cannot accurately capture the nonlinear deformation characteristics of the saw blade under high-speed rotation.

[0008] To achieve the above object, the application provides a high-speed circular sawing machine sawing method based on the least square method, comprising the following steps:

[0009] S1, collecting non-uniform point cloud data of the workpiece edge by using a laser scanner, and generating a discrete sampling point set of the workpiece edge containing N three-dimensional coordinate points;

[0010] S2, performing piecewise cubic spline interpolation processing on the discrete sampling point set to generate a continuous and derivable cutting reference curve;

[0011] S3, constructing a mathematical model with the sum of square errors of the kerf trajectory as the objective function, the model taking the saw blade speed n, the feed speed v and the sawing depth d as the optimization variables, and introducing the sawing force F as the constraint condition;

[0012] S4, based on the mathematical model and the cutting reference curve, adjusting the saw blade speed n, the feed speed v and the sawing depth d through an iterative algorithm to make the sum of square errors of the kerf trajectory converge under the constraint condition of the sawing force F, and obtaining an optimal process parameter combination (n, v, d*);

[0013] S5, controlling the sawing blade operation according to the optimal process parameter combination;

[0014] In the step S4, the iterative algorithm adopts the Newton iteration method, and the specific operation process is as follows:

[0015] S41, giving the initial saw blade speed n0, the feed speed v0 and the sawing depth d0 as the iteration starting point;

[0016] S42, calculating the sum of square errors of the kerf trajectory and its partial derivatives with respect to n, v and d according to the process parameter values of the current iteration point;

[0017] S43, updating the values of the process parameters by using the Newton iteration formula to obtain a new iteration point;

[0018] S44, judging whether the new iteration point meets the convergence condition, if yes, stopping the iteration and outputting the optimal process parameter combination (n, v, d*); if not, returning to step S42 for continuous iteration.

[0019] Preferably, the cutting reference curve is any one of the following or a combination of the two:

[0020] (a) a V-shaped notch composed of two straight line segments;

[0021] (b) a U-shaped notch composed of a local circular arc.

[0022] Preferably, the quantification method of the sum of square errors of the kerf trajectory is:

[0023]

[0024] wherein, P i is the coordinate of a point on the theoretical cutting trajectory at time t i is a three-dimensional coordinate vector of the i-th sampling point collected by the laser scanner, satisfying i P i-1 ||≤Δs max (2,...N), is the maximum allowed point spacing of the scanner; n i P i is the unit principal normal vector of the theoretical trajectory curve at time t i points to the outside of the curve for convex curve segments; n i points to the inside of the curve for concave curve segments; and the normal vector direction of straight line segments is pre-set according to the material properties of the workpiece.

[0025] Preferably, the expression of the mathematical model is:

[0026]

[0027] The constraint condition is:

[0028] for representing the component of the sawing force in the machining plane;

[0029] and for representing the boundary of the feasible region of the process parameters;

[0030] wherein, is the normal error component of the kerf trajectory defined above, and its expression is

[0031] Preferably, the is a C 2 continuous three-dimensional curve generated by cumulative chord length parameterization spline interpolation of the laser scanning point cloud, and the spline interpolation adopts clamped boundary conditions, satisfying conditions, and v0 and v1 are determined by the workpiece feeding direction.

[0032] Preferably, before step S2 is performed, the discrete sampling point set is first subjected to down-sampling processing, and the down-sampling factor is adaptively determined according to the workpiece edge size and the point distribution density, and the value range is 0.1 to 0.5.

[0033] Preferably, the condition for determining whether the convergence state is reached in the step S4 comprises: the difference of the squared sum of the kerf trajectory errors obtained by two continuous iterations is less than a preset threshold value e1, and the variation of the process parameters obtained by two continuous iterations is less than a preset threshold value e2, wherein e1 and e2 are positive numbers.

[0034] Preferably, the threshold value e1 is in the range of 1x10 -6 mm 2 ~ 1x10 -3 mm 2 , and the threshold value e2 is in the range of 0.1% to 1%, wherein e2 represents the relative variation rate of the variation of the process parameters.

[0035] Preferably, in the step S42, when calculating the squared sum of the kerf trajectory errors, the i-th sampling point coordinates collected by the laser scanner are verified:

[0036] If the chord length formed by the point and its adjacent points is greater than twice the maximum allowed point spacing, the point is removed in real time and a new sampling point is supplemented by using linear interpolation method to ensure the accuracy of error calculation.

[0037] To achieve the above-mentioned purpose, the present application provides a high-speed circular sawing machine sawing system for realizing any one of the above-mentioned high-speed circular sawing machine sawing methods based on the least square method, comprising:

[0038] a laser scanner configured to collect non-uniform point cloud data of the workpiece edge to generate a discrete sampling point set of the workpiece edge edge containing N three-dimensional coordinate points;

[0039] a data processing unit in communication connection with the laser scanner and configured to: perform piecewise cubic spline interpolation processing on the discrete sampling point set to generate a continuous and derivable cutting reference curve; construct a mathematical model with the squared sum of the kerf trajectory errors as the objective function, the model taking the saw blade speed n, the feed speed v and the sawing depth d as the optimization variables, and introducing the sawing force F as the constraint condition; based on the mathematical model and the cutting reference curve, adjusting the saw blade speed n, the feed speed v and the sawing depth d by Newton iteration method to make the squared sum of the kerf trajectory errors converge under the constraint condition of the sawing force F, and obtaining the optimal process parameter combination (n, v, d*).

[0040] a controller in communication connection with the data processing unit and the circular sawing machine and configured to control the speed of the sawing blade, the feed speed of the workbench and the sawing depth according to the optimal process parameter combination (n, v, d*).

[0041] a sawing force monitoring device configured to monitor the sawing force F in the processing process in real time and feed the force signal to the data processing unit for applying the sawing force constraint in the iterative optimization process.

[0042] The circular saw machine actuator includes a sawing motor, a feed driving mechanism and a depth adjusting mechanism, which are controlled by the controller to perform sawing operations.

[0043] The technical scheme of the present application has the following beneficial effects:

[0044] The laser scanner obtains non-uniform point cloud data of the workpiece edge, and a C2 continuous cutting reference curve is generated by combining piecewise cubic spline interpolation, which can accurately restore any complex geometric features and effectively solve the problem of corner distortion caused by traditional linear approximation.

[0045] The piecewise cubic spline interpolation (C 2 The spline interpolation with clamped boundary conditions ensures that the starting point and the ending point of the curve strictly pass through the key control points set in the workpiece feed direction, and eliminates the end oscillation phenomenon.

[0046] The square sum of the cutting trajectory error is introduced as the objective function, and the gradient descent direction is efficiently solved by the Newton iteration method, so that when processing special-shaped parts with multiple concave and convex surfaces, the non-uniform point cloud data collected by the laser scanner can fully reflect the edge features of the part. After the piecewise cubic spline interpolation processing, the cutting reference curve closely fits the actual contour of the part.

[0047] In the iterative optimization process, the Newton iteration method quickly converges to the optimal process parameter combination, so that the saw blade can run along the ideal trajectory during cutting. And through the reasonable matching of the saw blade speed n, the feed speed v and the sawing depth d, not only the quality of the cut is guaranteed, but also the production efficiency is greatly improved. At the same time, since the sawing force F is introduced as a constraint condition, the problems of rapid tool wear and workpiece deformation caused by improper process parameter setting are effectively avoided. BRIEF DESCRIPTION OF DRAWINGS

[0048] Figure 1 The flowchart of the embodiment of the present application subject matter;

[0049] Figure 2 The workpiece edge three-dimensional point cloud distribution diagram obtained based on laser scanning of the embodiment of the present application subject matter.

[0050] The implementation, functional features and advantages of the present application will be further described with reference to the embodiments and the accompanying drawings. DETAILED DESCRIPTION

[0051] The scheme in the embodiments of the present application will be described in detail below with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments of the present application, all other embodiments obtained by those of ordinary skill in the art without creative effort belong to the scope of the present application.

[0052] It should be noted that all directional indications, such as upper, lower, left, right, front, back, etc., in the embodiments of the present application are only used to explain the relative position relationship, movement condition, etc. between components in a certain posture (as shown in the drawings), and if the certain posture changes, the directional indications also change accordingly.

[0053] It should also be noted that when an element is referred to as being "fixed to" or "set on" another element, it can be directly on the other element or can have a middle element. When an element is referred to as being "connected" to another element, it can be directly connected to the other element or can have a middle element.

[0054] In addition, if the present application involves "first", "second", etc. description, it is only for description purpose (such as for distinguishing the same or similar elements), and cannot be understood as indicating or implying the relative importance of the indicated technical features or implicitly indicating the number of the indicated technical features. Therefore, the features limited by "first", "second" can explicitly or implicitly include at least one of the features. In addition, the technical solutions of each embodiment can be combined with each other, but it must be based on the realization of those of ordinary skill in the art, and when the combination of technical solutions appears contradictory or unachievable, it should be considered that the combination of technical solutions does not exist, and is not within the protection scope of the present application.

[0055] Referring to Figure 1 The present application proposes a high-speed circular sawing machine sawing method based on least square method, comprising the following steps:

[0056] S1, collecting non-uniform point cloud data of the workpiece edge by using a laser scanner, generating a discrete sampling point set of the workpiece edge containing N three-dimensional coordinate points;

[0057] S2, performing piecewise cubic spline interpolation processing on the discrete sampling point set to generate a continuous and derivable cutting reference curve;

[0058] S3, constructing a mathematical model with the sum of square errors of the cut trajectory as the objective function, the model taking the saw blade speed n, the feed speed v and the sawing depth d as the optimization variables, and introducing the sawing force F as the constraint condition;

[0059] S4, adjusting the saw blade rotation speed n, the feed speed v and the sawing depth d by an iterative algorithm based on the mathematical model and the cutting reference curve, converging the incision trajectory error sum of squares under the constraint condition of the sawing force F to obtain an optimal process parameter combination (n, v, d*); S5, controlling the sawing blade operation according to the optimal process parameter combination.

[0060] S5, controlling the sawing blade operation according to the optimal process parameter combination.

[0061] The iterative algorithm in the step S4 adopts the Newton iteration method, and the specific operation process is as follows:

[0062] S41, giving an initial saw blade rotation speed n0, an initial feed speed v0 and an initial sawing depth d0 as an iterative starting point;

[0063] S42, calculating the incision trajectory error sum of squares and the partial derivatives thereof with respect to n, v and d according to the process parameter values of the current iterative point;

[0064] S43, updating the process parameter values by using the Newton iteration formula to obtain a new iterative point;

[0065] S44, judging whether the new iterative point meets the convergence condition, if yes, stopping the iteration and outputting the optimal process parameter combination (n, v, d*); if not, returning to the step S42 for continuous iteration.

[0066] For example, the non-uniform point cloud data of the workpiece edge is collected by using a laser scanner to generate a workpiece edge discrete sampling point set containing a plurality of three-dimensional coordinate points; and the mathematical model is obtained Figure 2 .

[0067] The Figure 2 is a workpiece edge three-dimensional point cloud distribution diagram obtained based on laser scanning, wherein the discrete sampling points are arranged in a non-uniform space, and intuitively reflect the geometric complexity of the actual workpiece surface and the randomness characteristics of the measurement data. Through the comparison between the high-density area and the sparse area, the natural sampling density difference of the workpiece contour in different curvature sections is clearly shown - dense measurement point groups are automatically formed at the convex and concave transition parts with large curvature, and loose distribution patterns are presented at the relatively flat straight line sections. This non-uniformity not only retains the detail features of the original topography, but also provides a real data basis for the subsequent construction of the C 2 Continuous cutting reference curve provides a real data basis.

[0068] Further observation shows that there are local outliers and noise interference in the point cloud, but the overall edge topology remains recognizable. The original measurement feature described above can effectively suppress the fitting distortion phenomenon caused by uneven sampling density after cumulative chord length parameterization processing. Combined with the constraint mechanism of clamped boundary conditions, the first and last key control points can be precisely anchored to ensure that the generated spline curve strictly passes through the preset process start and end positions, thereby eliminating the oscillation error generated by traditional free-end point interpolation.

[0069] The workpiece edge discrete sampling point set is preprocessed, including noise filtering to eliminate obvious outliers and random noise points, and retaining effective data; then cumulative chord length parameterization resampling operation is implemented, so that the non-uniformly distributed original point cloud is converted into a new sequence with uniform spacing characteristics for eliminating the interference of unequal original point distance on curve fitting and improving the stability and accuracy of subsequent interpolation calculation. And through piecewise cubic spline interpolation technology, the first and second derivatives of the first and last endpoints are constrained according to the clamped boundary condition, and a smooth reference curve meeting the C2 continuity requirement is constructed.

[0070] The quantitative method of the cut trajectory error square sum is:

[0071]

[0072] Wherein, P i represents the point coordinates on the theoretical cutting trajectory at t i time, P i represents the three-dimensional coordinate vector of the i-th sampling point coordinates collected by the laser scanner, satisfying ||P i-1 ||≤Δs max (2,…N), is the maximum allowed point spacing of the scanner; n i represents the unit principal normal vector of the theoretical trajectory curve at t i time, the direction of which is from the center of curvature of the curve to the point; and for convex curve segment n i points to the outside of the curve; for concave curve segment n i points to the inside of the curve; and the normal vector direction of the straight line segment is pre-set according to the material characteristics of the workpiece.

[0073] Further, the expression of the mathematical model is:

[0074]

[0075] The constraint condition is:

[0076] Used to represent the component constraint of sawing force in the machining plane;

[0077] and for representing the boundary of the feasible region of the process parameters;

[0078] wherein, is the normal error component of the cut trajectory defined above, whose expression is

[0079] the is the C2 continuous cut reference curve generated by the cumulative chord length parametric spline interpolation of the laser scanner point cloud. 2 a continuous three-dimensional curve, and the spline interpolation adopts a clamped boundary condition, satisfying the condition of , and v0 and v1 are determined by the workpiece feeding direction.

[0080] In this embodiment, the non-uniform point cloud data of the workpiece edge is obtained by the laser scanner, and a C2 continuous cut reference curve is generated by combining the piecewise cubic spline interpolation, which can accurately restore any complex geometric features, and effectively solves the problem of corner distortion caused by traditional linear approximation. Especially for the area with sudden change of curvature, the dynamic adjustment mechanism of the unit principal normal vector direction ensures the accurate control of the normal error component. The piecewise cubic spline interpolation (C2 continuous) cooperates with the clamped boundary condition to realize high-precision fitting of the non-uniform point cloud data; the spline interpolation of the clamped boundary condition ensures that the starting point and the ending point of the curve strictly pass through the key control points set by the workpiece feeding direction, eliminating the end oscillation phenomenon. Compared with the traditional B-spline or linear interpolation, this method effectively suppresses the local distortion caused by uneven sampling density while ensuring the curvature continuity.

[0081] On the other hand, the cut trajectory error square sum is introduced as the objective function, and its gradient descent direction is efficiently solved by the Newton iteration method, so that when processing special-shaped parts with multiple concave and convex surfaces, the non-uniform point cloud data collected by the laser scanner can fully reflect the edge features of the part. After the piecewise cubic spline interpolation, the cut reference curve obtained is closely fitted to the actual contour of the part. During the iterative optimization process, the Newton iteration method quickly converges to the optimal process parameter combination, so that the saw blade can run along the ideal trajectory during cutting. Through the reasonable matching of the saw blade speed n, the feed speed v and the sawing depth d, not only the quality of the cut is guaranteed, but also the production efficiency is greatly improved. At the same time, since the sawing force F is introduced as a constraint condition, the problems of excessive tool wear and workpiece deformation caused by improper process parameter setting are effectively avoided. In the process of converging the cut trajectory error square sum while meeting the constraint condition, the adjustment of each process parameter is calculated accurately. For example, when encountering a part with large curvature, the system will automatically reduce the feed speed v appropriately, while adjusting the saw blade speed n and the sawing depth d, to ensure that the sawing force remains within a reasonable range, preventing damage to the workpiece or tool due to excessive force.

[0082] In summary, the method realizes intelligent matching of saw blade speed, feed speed and sawing depth, which not only ensures the quality of the cut but also improves the production efficiency. Especially for the concave-convex surface features of special-shaped parts, the system can automatically adjust the process parameter combination, actively reduce the feed speed in the area with large curvature and optimize the cutting load distribution, effectively preventing workpiece deformation and tool abnormal wear.

[0083] In one embodiment, the cutting reference curve is any one of the following or a combination of both:

[0084] (a) V-shaped notch composed of two straight line segments;

[0085] (b) U-shaped notch composed of a local circular arc.

[0086] In this embodiment, when scheme (a) is selected, the two straight line segments of the V-shaped notch realize C 2 continuous transition, and the curvature radius at the intersection tends to infinity to avoid stress concentration; in scheme (b), the circular arc segment of the U-shaped notch also satisfies the C2 continuity requirement with the adjacent straight line segment, and the adaptive node distribution algorithm optimizes the matching relationship between the circular arc radius and the chord length. At the same time, the clamped boundary conditions of the two structures force the curve to pass through the preset starting point and ending point control points, ensuring accurate alignment with the workpiece coordinate system.

[0087] In one embodiment, before step S2 is performed, the discrete sampling point set is first subjected to downsampling processing, and the downsampling factor is adaptively determined according to the workpiece edge size and the point distribution density, with a value range of 0.1 to 0.5.

[0088] In this embodiment, before step S2 is performed, the discrete sampling point set is first subjected to downsampling processing, and the downsampling factor is adaptively determined according to the workpiece edge size and the point distribution density, with a value range of 0.1 to 0.5. This preprocessing process dynamically adjusts the sampling density based on the local curvature estimation algorithm - a higher compression ratio (close to 0.5) is used in flat areas, while more original data points are retained in high-curvature areas (the compression ratio is reduced to 0.1), which reduces the redundant calculation amount and ensures the geometric integrity of the key feature area. Through this non-uniform downsampling strategy, the subsequent piecewise cubic spline interpolation can maintain overall C 2 continuity while significantly improving the convergence speed and reducing memory usage.

[0089] Specifically, the special implementation of the V-shaped notch (scheme a) includes: implanting a virtual control point at the junction of the two straight line segments to form a pseudo-quadratic Bezier transition segment, so that the theoretically infinite curvature radius is realized in the form of a finite large number in actual calculation, and the Runge-Kutta integration method with adaptive step size is used to solve the differential equation set, ensuring numerical stability;

[0090] For the U-shaped notch (scheme b), a composite parameterization method is adopted to establish a mapping relationship between the angle increment of the circular arc segment and the chord length change rate, and the optimal node position is determined through golden section search, so that the connection between the circular arc and the straight line segment not only satisfies the C 2 continuous condition, but also minimizes the energy function jump across the segments.

[0091] In one embodiment, the condition for determining whether the convergence state is reached in step S4 includes: the difference between the squared sums of the kerf trajectory errors obtained by two consecutive iterations is less than a preset threshold value ε1, and the variation of the process parameters obtained by two consecutive iterations is less than a preset threshold value ε2, where ε1 and ε2 are positive numbers.

[0092] Further, the threshold value ε1 is in the range of 1x10 -6 mm 2 ~ 1x10 -3 mm 2 , and the threshold value ε2 is in the range of 0.1% to 1%, where ε2 represents the relative variation rate of the variation of the process parameters.

[0093] In one embodiment, when calculating the squared sum of the kerf trajectory errors in step S42, the coordinates of the i-th sampling point collected by the laser scanner are verified:

[0094] If the chord length formed by the point and its adjacent point is greater than twice the maximum allowed point spacing, the point is immediately removed, and a new sampling point is supplemented by linear interpolation to ensure the accuracy of the error calculation.

[0095] In this embodiment, when it is detected that the chord length Li formed by a sampling point i and its adjacent point exceeds twice the maximum allowed point spacing Dmax, the system will trigger a three-level response mechanism: first, the abnormal point is immediately removed, then a replacement point is generated based on the coordinates of the front and rear valid points by linear interpolation, and finally the local curvature of the region is checked again. Thus, while maintaining the integrity of the overall data, the discrete noise caused by equipment jitter or environmental interference is effectively suppressed.

[0096] The present application proposes a high-speed circular sawing machine sawing system for implementing the high-speed circular sawing machine sawing method based on the least square method as claimed in any one of the above, comprising:

[0097] a laser scanner configured to collect non-uniform point cloud data of the workpiece edge to generate a discrete sampling point set of the workpiece edge edge containing N three-dimensional coordinate points;

[0098] a data processing unit, in communication with the laser scanner, configured to: perform piecewise cubic spline interpolation on the discrete sampling point set to generate a continuous and derivable cutting reference curve; construct a mathematical model with the sum of squared kerf trajectory errors as an objective function, the model taking saw blade rotation speed n, feed speed v and sawing depth d as optimization variables and introducing sawing force F as a constraint condition; based on the mathematical model and the cutting reference curve, adjust the saw blade rotation speed n, the feed speed v and the sawing depth d through Newton iteration method to make the sum of squared kerf trajectory errors converge under the constraint condition of the sawing force F, and obtain an optimal process parameter combination (n, v, d*); a controller, in communication with the data processing unit and the circular saw machine, configured to control the rotation speed of the sawing blade, the feed speed of the workbench and the sawing depth according to the optimal process parameter combination (n, v, d*); a sawing force monitoring device, configured to monitor the sawing force F in real time during the machining process and feed the force signal to the data processing unit for applying the sawing force constraint in the iterative optimization process; and a circular saw machine execution mechanism, including a sawing motor, a feed driving mechanism and a depth adjusting mechanism, controlled by the controller to perform the sawing operation.

[0099]

[0100]

[0101]

[0102] The above only describes some or preferred embodiments of the present application, neither the text nor the drawings can limit the scope of protection of the present application, any equivalent structural transformation based on the content of the present application specification and drawings or direct / indirect application in other related technical fields is included in the scope of protection of the present application.​​​

Claims

1. A high-speed circular sawing method based on the least square method, characterized by, The method comprises the following steps: S1, collecting non-uniform point cloud data of the workpiece edge by using a laser scanner to generate a discrete sampling point set of the workpiece edge containing N three-dimensional coordinate points; S2, performing piecewise cubic spline interpolation processing on the discrete sampling point set to generate a continuous and derivable cutting reference curve; S3, constructing a mathematical model with the sum of squared kerf trajectory errors as an objective function, the model taking the saw blade rotation speed n, the feed speed v and the sawing depth d as optimization variables, and introducing the sawing force F as a constraint condition; S4, based on the mathematical model and the cutting reference curve, adjusting the saw blade rotation speed n, the feed speed v and the sawing depth d through an iterative algorithm to make the sum of squared kerf trajectory errors converge under the constraint condition of the sawing force F, and obtaining an optimal process parameter combination (n, v, d*); S5, controlling the sawing blade operation according to the optimal process parameter combination; In the step S4, the iterative algorithm adopts the Newton iteration method, and the specific operation process is as follows: S41, giving an initial saw blade rotation speed n0, an initial feed speed v0 and an initial sawing depth d0 as an iteration starting point; S42, calculating the sum of squared kerf trajectory errors and its partial derivatives with respect to n, v and d according to the process parameter values of the current iteration point; S43, updating the values of the process parameters by using the Newton iteration formula to obtain a new iteration point; S44, judging whether the new iteration point meets the convergence condition, if yes, stopping the iteration and outputting the optimal process parameter combination (n, v, d*); if not, returning to the step S42 for continuous iteration.

2. A high speed circular sawing method based on least square method as claimed in claim 1 wherein, The cutting reference curve is any one of the following or a combination of the two: (a) a V-shaped notch composed of two straight line segments; (b) a U-shaped notch composed of a local circular arc.

3. A high speed circular sawing method based on least square method as claimed in claim 1 wherein, The quantification method of the sum of squared kerf trajectory errors is as follows: wherein, denotes the point coordinate on the theoretical cutting trajectory at time t i denotes the point coordinate on the theoretical cutting trajectory at time t i denotes the three-dimensional coordinate vector of the i-th sampling point coordinate collected by the laser scanner, satisfying ||P i -P i-1 ||≤Δs max (2,...N), is the maximum allowable point spacing of the scanner; n i denotes the point coordinate on the theoretical cutting trajectory at time t i denotes the unit principal normal vector of the theoretical trajectory curve at time t i points to the outside of the curve; for a concave curve segment n i points to the inside of the curve; and the normal vector direction of a straight line segment is predetermined according to the material properties of the workpiece.

4. The high speed circular sawing method based on least square method according to claim 1, wherein, The expression of the mathematical model is as follows: The constraint condition is as follows: for indicating a component of the sawing force in the machining plane is constrained; and for representing the boundaries of the process parameter feasible region; wherein is the above defined cut trajectory normal error component, which is expressed as 5. A high speed circular sawing machine sawing method based on least square method according to claim 1, characterized in that, The C 2 continuous three-dimensional curve, and the spline interpolation adopts a clamped boundary condition, and meets conditions, and v0 and v1 are determined by the workpiece feeding direction.

6. A high speed circular sawing machine sawing method based on least square method according to claim 2, characterized in that, Before the step S2 is performed, the discrete sampling point set is first subjected to downsampling processing, and the downsampling factor is adaptively determined according to the workpiece edge size and the point distribution density, and the value range is 0.1 to 0.

5.

7. A high speed circular sawing machine sawing method based on least square method according to claim 3, characterized in that, The conditions for judging whether the convergence state is reached in the step S4 include that the difference between the sum of squared kerf trajectory errors obtained by continuous two iterations is less than a preset threshold value ε1, and the variation of the process parameters obtained by continuous two iterations is both less than a preset threshold value ε2, wherein ε1 and ε2 are both positive numbers.

8. A high speed circular sawing machine sawing method based on least square method according to claim 4, characterized in that, The threshold value ε1 ranges from 1 x 10 -6 mm 2 to 1 x 10 -3 mm 2 , and the threshold value ε2 ranges from 0.1% to 1%, where ε2 represents a relative change rate of the process parameter variation amount.

9. The high speed circular sawing machine sawing method based on least square method according to claim 1, characterized in that, In the step S42, when calculating the sum of squared kerf trajectory errors, the i-th sampling point coordinate collected by the laser scanner is verified: If the chord length formed by the point and its adjacent points is greater than 2 times the maximum allowed point spacing, the point is real-time removed and a new sampling point is supplemented by using a linear interpolation method to ensure the accuracy of error calculation.

10. A high-speed circular saw machine sawing system for implementing the least squares based high-speed circular saw machine sawing method according to any one of claims 1-9, characterized by, The method comprises the following steps: A laser scanner; configured to collect non-uniform point cloud data of the workpiece edge to generate a discrete sampling point set of the workpiece edge containing N three-dimensional coordinate points; a data processing unit; In communication connection with the laser scanner, configured to: perform piecewise cubic spline interpolation processing on the discrete sampling point set to generate a continuous and derivable cutting reference curve; construct a mathematical model with the square sum of kerf trajectory error as the objective function, the model taking the saw blade rotation speed n, the feed speed v and the sawing depth d as optimization variables, and introducing the sawing force F as a constraint condition; Based on the mathematical model and the cutting reference curve, the saw blade rotation speed n, the feed speed v and the sawing depth d are adjusted through Newton iteration method to make the square sum of kerf trajectory error converge under the constraint condition of sawing force F, and the optimal process parameter combination (n, v, d*) is obtained; A controller in communication connection with the data processing unit and the circular saw machine, configured to control the rotation speed of the sawing blade, the feed speed of the workbench and the sawing depth according to the optimal process parameter combination (n, v, d*); A sawing force monitoring device configured to monitor the sawing force F in the processing process in real time and feed the force signal to the data processing unit for applying the sawing force constraint in the iterative optimization process; A circular saw machine actuator including a sawing motor, a feed driving mechanism and a depth adjusting mechanism, controlled by the controller to perform the sawing operation.

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