Residual height tool path generation method for free-form surface three-axis numerical control machining

Abstract

The application discloses a free-form surface three-axis numerical control machining equal residual height tool path generation method, which comprises the following steps: firstly, introducing a free-form surface model to be machined, setting machining tool, maximum allowed value of residual height and other information; then, constructing a local coordinate system for a current tool path point, obtaining a residual height point on the surface model by using an intersection method, and calculating a related curve segment, and calculating the residual height point on the tool contour by using an iteration method; constructing a local coordinate system for the residual height point, calculating a coordinate initial value of the residual height tool path point, and iteratively calculating a next row residual height tool path point according to the distance between the tool path point and the surface model. Through the above method, the application provides a free-form surface three-axis numerical control machining equal residual height tool path generation method, which does not need to perform equidistance on the surface, and realizes direct and efficient calculation of the equal residual height tool path for the free-form surface.

Description

Technical Field

[0001] This invention belongs to the technical field of Computer Aided Manufacturing (CAM), specifically relating to a method for generating residual height toolpaths in freeform surface three-axis CNC machining. Background Technology

[0002] Unlike commonly used toolpath generation methods such as the line spacing adaptive method and the equal line spacing method, the equal residual height toolpath controls the distance between adjacent tool points to ensure that the residual height is always at the maximum allowable value, thereby maximizing the line spacing and minimizing the total toolpath length. It is particularly suitable for machining free-form surface products with smooth surface transitions.

[0003] Equal residual height CNC machining toolpaths offer significant advantages in machining efficiency and surface residual height uniformity. The main process for calculating equal residual height toolpaths involves determining the residual height points and then using these points to calculate the equal residual height toolpath positions. However, the geometric characteristics of residual height are complex, making the calculation of residual height points and equal residual height toolpath positions difficult. Furthermore, each row of toolpath positions needs to be calculated individually based on the previous row, resulting in a large computational load. Currently, most methods for generating three-axis equal residual height CNC machining toolpaths are designed for triangular meshes and point cloud models. The few available surface algorithms generally require equidistant and intersection calculations on the surface, often leading to anomalies in areas with excessively high or low curvature. Algorithms that directly generate equal residual height toolpaths for free-form surfaces are also rare.

[0004] Chinese patent application CN201810224947.9 discloses a method for generating tool contact trajectories with equal residual height using a triangular mesh model. This method generates tool contact trajectories by dividing tool contact points into three types, applying anisotropic bias to the tool contact points to obtain corresponding biased tool contact points, and performing self-intersection processing on the biased tool paths. It proposes that for different types of tool contact points, the actual bias point is calculated based on anisotropic bias within the tool contact point's tangential plane. Then, self-intersection detection, intersection point calculation, and effective sub-path judgment are performed on the biased tool contact trajectories, ultimately making the machining residual height between tool trajectories closer to the maximum allowable value. Chinese patent application CN201410597489.5 discloses a method for generating and optimizing tool contact trajectories with equal residual height for five-axis CNC machining. This method, targeting five-axis machining of complex mesh models, proposes an adaptive projection offset method to generate five-axis residual tool contact point trajectories. It then performs trajectory smoothing, trajectory point optimization, and trajectory self-intersection removal on the tool trajectory, ultimately obtaining a more ideal tool contact point trajectory. Chinese patent application number CN201910618075.9 discloses a method for generating CNC machining toolpaths with equal residual height on three axes from a point cloud model. This method eliminates the need for point cloud offsetting or surface reconstruction, achieving direct and efficient calculation of residual height toolpaths from the point cloud.

[0005] The above patents are all for triangular meshes and point cloud models. Currently, the few surface algorithms generally require equidistant and intersection calculations on the surface, which often leads to anomalies in areas with excessively large or small curvature. There are very few algorithms that can directly generate residual toolpaths for freeform surfaces. Summary of the Invention

[0006] Currently, no commercial CAM software can directly calculate the toolpath for three-axis CNC machining with equal residual height on freeform surfaces. The main technical problem solved by this invention is to provide a method for generating toolpaths with equal residual height for three-axis CNC machining of freeform surfaces. By directly generating residual height points on the freeform surface, and to improve computational efficiency, an adaptive discretization method is proposed. This method uses a set of discrete feature points, including the golden section point, to reduce the number of discretization iterations, thereby obtaining the residual height points iteratively. To further improve computational efficiency, a new method for calculating the initial tool position point is proposed, and the adaptive discretization method is used again to obtain the minimum distance point from the intersecting surface to the tool position point, thus obtaining the target tool position point with equal residual height. Finally, the toolpath with equal residual height is generated.

[0007] The technical solution adopted in this invention is: to provide a method for generating residual height toolpaths in free-form surface three-axis CNC machining, including the following specific steps:

[0008] Step 1: Input the freeform surface model to be machined and the machining parameters, and calculate the set of tool positions for the first pass;

[0009] Let the initial toolpath of the curve be... Let be the curve of the longest side of the freeform surface. Equal-error toolpaths are generated on this curve to obtain the set of tool contact points. The normal vector is calculated for each tool contact point using the k-nearest neighbor method. The set of the first-row tool positions is calculated according to equation (1). ;

[0010] (1)

[0011] Step 2: Construct a local coordinate system at the tool setting point;

[0012] Let the first The set of cutting points is , ,by Create a local coordinate system for the origin. Let vector for The positive direction of the axis, the normal plane is the coordinate plane. , and the global coordinate plane The intersection line as The axis is finally determined using the right-hand rule. Axis; let , , The unit vectors of the axes are respectively , , It can be obtained from equation (2).

[0013] (2)

[0014] any point Coordinates in the local coordinate system It can be obtained from equation (3).

[0015] (3)

[0016] Step 3: Obtain the local free curve segment on the feed direction normal plane;

[0017] Let the plane With freeform surfaces Intersect at curve Because the residual height point is in the line spacing direction, it is in the local coordinate system middle, The value should be within In the positive direction, that is, satisfying ,in correspond in positive direction point , Corresponding to points With center at and radius at, circle Intersection with the curve .

[0018] Step 4: Iteratively calculate the residual height points;

[0019] Step 4.1: Obtain the discrete feature point set on the local free curve segment. Let the parameter region on the curve segment be... , and Each of the interval endpoints is a separate endpoint. and In free curve The parameters on, The number of iterations for this process, its initial discrete number is: That is, at this time, the endpoints of the parameter region correspond to the first point. and the end point The discrete feature point set of the curve segment is obtained by using equation (4). ,in .

[0020] (4)

[0021] Its corresponding point In free curve The parameters can be calculated using equation (5);

[0022] (5)

[0023] for In the interval The position coefficients in the middle are the first and last point coefficients, respectively. , coefficients at intermediate parameter points The coefficients of the two golden ratio points , First discrete feature point set .

[0024] Step 4.2: Obtain the residual height points corresponding to the discrete feature point set; using the discrete feature point set... With each point in the middle as the center, the maximum allowable residual height is... Draw a circle with radius 1. , intersecting the tool circle Assume a set of points. One of the points is Its corresponding residual height point The coordinates are The coordinates of the intersection point are obtained by using equation (6).

[0025] (6)

[0026] For the two calculated intersection points and ,like Then point The residual height points of discrete feature points are added to the point set. Otherwise click The residual height points of discrete feature points are added to the point set. And calculate the point set according to equation (7). The point with the largest value on the horizontal axis is taken as the point with the same residual height. .

[0027] (7)

[0028] Step 4.3: Determine whether the residual height points meet the requirements; based on the residual height points... Centered on the circle, with the maximum allowable residual height as the center, respectively and minimum allowable value Concentric circles with radius Based on the analysis in step 4.2, concentric circles... With free curves Intersecting, with concentric circles There must be one point among the intersection points of the outer circles that lies in the discrete feature point set. In, if and only if concentric circles When the outer circle intersects the free curve and the inner circle separates from the free curve, the residual height point is the target residual height point, and proceed to step 4.4. Otherwise, the requirement for equal residual accuracy is not met, and at this time, the concentric circles... The outer circle intersects the free curve at two points, denoted as and respectively. and Get this time and The coordinates are used, and the curve segment between the two points is taken as the next local free curve region. Returning to step 4.1, if at this point... And because of concentric circles In a circle Internal, therefore it is located inside In the negative direction, therefore the endpoints Calculated as the left endpoint of the iteration region, i.e. .

[0029] Step 4.4: Construct a local coordinate system for the residual height points; the above process can obtain points with equal residual height. The local coordinates of the can be obtained from the global coordinates using equation (8).

[0030] (8)

[0031] Step 5: Construct a local coordinate system for the remaining height points;

[0032] Let the first The set of residual height points is , Similar to step 2, with Create a local coordinate system for the origin. Let vector for The positive direction of the axis, the normal plane is the coordinate plane. , and the global coordinate plane The intersection line as The axis is finally determined using the right-hand rule. Axis, find , , Unit vector of the axis , , , and the coordinates of the point in the local coordinate system;

[0033] Step 6: Set the initial coordinates of the tool position points with equal residual height;

[0034] Step 6.1: Select the region containing the initial value of the tool position point with equal residual height; obtain the plane. Intersection with freeform surface , with residual height points With the center of the circle, Construct a circle with radius . Its satisfaction Due to the tool position point The center of the tool circle is the point through which the tool circle passes. ,and lie in In the positive direction, the tool position point must be located in the circle. an arc on the top Above, that is ,in Represents a circle any point on corresponding and The counterclockwise angle in the positive direction, the endpoint of the region. and Local coordinate systems median coordinate and point

[0035] Step 6.2: Obtain the region where the initial value of the tool position point is located; it is known that the initial value of the tool position point is located on an arc. Above, its Angle range is And the two endpoints of the arc are and During the first loop , .

[0036] Step 6.3: Obtain the discrete feature point set on the arc region; the discrete feature point set of the arc region is... It can be obtained from equation (9). .

[0037] (9)

[0038] in For the corresponding and The counterclockwise angle in the positive direction can be calculated using equation (10).

[0039] (10)

[0040] for In the interval The position coefficients in the middle are the coefficients of the first and last points, respectively. , The coefficients of the midpoint parameter points The coefficients of the two golden ratio points , .

[0041] Step 6.4: Determine whether the points in the discrete feature point set meet the accuracy requirements; in the point set... middle, and The two corresponding points are boundary points, which in the iteration process are the points in the previous loop and the curve, respectively. The centers of the tool circles that are completely intersecting and completely disjoint are not included in the calculation during the iteration process; only the centers are discussed. ,from Start in sequence, with Centered on the circle, with the tool radius as the center, respectively and precision radius For radius, Draw a concentric tool circle given the user's radius accuracy. until satisfied concentric cutting tool circle Inner and outer circles and curves Separated. At this time, and As the arc region in the next iteration The boundary points are re-recorded as points. and Proceed to step 6.2. Record the concentric tool circle. Outer circle and curve If the inner circle of the two objects intersects but the inner circle of the two objects is not to each other, then they can be considered tangent, which satisfies the accuracy requirements and obtains the initial value of the desired equal residual height tool position. Its corresponding tangent point is If concentric circles at this time Outer circle and curve Intersect at two points and tangent point for perpendicular bisector and free curve of the line The intersection point.

[0042] Step 7: Iteratively calculate the knife point with equal residual height;

[0043] Step 7.1: Obtain the initial tool position point and known points on intersecting surfaces Assuming the tool is at the initial tool position... The point intersects with the freeform surface. According to Section 2.1, there exists a known point on the intersecting surface. That is, the tangent point .

[0044] Step 7.2: Obtain the initial discrete directions of known points on the intersecting surfaces. ; Obtain known points on the intersecting surfaces according to equation (11) of , parameter and In the parameter direction respectively , , and Increase parameter increment Four new points can be obtained by calculating using equations (11) and (12);

[0045] (11)

[0046] (12)

[0047] according to , , and Directional order constitutes a point set , The degree of local surface discretization. Calculate the point set The set of distances from each point in the middle to the tool's cutting point The minimum distance is Calculated by equation (13);

[0048] (13)

[0049] Its corresponding point Let it be the point of minimum distance. Initial discrete direction Based on the minimum distance point correspond The value is obtained by taking the minimum distance point at this time. Corresponding Then the initial discrete order Initial discrete direction for Direction, otherwise At that time, the initial discrete order Initial discrete direction for direction.

[0050] Step 7.3, for Discretize feature points along the parameter direction; because for Feature points are discretized along the parameter direction, hence the number of discretization operations. Assuming at this time... Parameter direction is Parameter direction, and passes through the minimum distance point The curve intersects the boundary of the intersecting surface at... and The curve segment is obtained by calculating according to equation (11). The corresponding new parameter area is The point with the smallest distance At the initial discrete time, it is According to equation (14), the parameter region Discretize the feature points;

[0051] (14)

[0052] Its point set is , ,in For point The parameters on the tool contact point trajectory line can be calculated using equation (15);

[0053] (15)

[0054] for In the interval The position coefficients in the middle are the coefficients of the first and last points, respectively. , The coefficients of the three quadrature parameter points , , The coefficients of the two golden ratio points , And calculate the discrete feature point set. From each feature point to the tool's cutting point Distance between The minimum distance is calculated according to equation (13) as follows: The minimum distance point is ,like Parameter direction is Parameter direction, and The calculation process for the parameter direction is the same.

[0055] Step 7.4: Determine the point of minimum distance Does the accuracy meet the requirements? and When, then the minimum distance point This can be denoted as the point of minimum distance from the intersecting surfaces to the tool point. The minimum distance is Otherwise, minimum distance point The accuracy does not meet the requirements; assume discrete direction. and discrete degree Correlation, when discrete order When the number is odd, the discrete direction is Direction, or conversely, discrete order When the number is even, the discrete direction is then... Direction. Then, based on the discrete order... Regain Discrete Direction Return to step 7.3.

[0056] Step 7.5: Determine the point of minimum distance on the surface. Does the residual accuracy meet the requirements? If the minimum distance point on the curved surface meets the residual height accuracy requirements, that is... This indicates that the tool position point with the same residual height is the same as the target tool position point with the same residual height. Proceed to step 7.7. Otherwise, if the minimum distance point does not meet the residual accuracy requirements, continue the iteration.

[0057] Step 7.6: Based on the minimum distance point on the surface Regain the same residual height tool position To facilitate calculations, a local coordinate system is selected. First of all On the plane, based on the residual height point With the center of the circle, Draw a circle with radius 1. At the same time, at the point of minimum distance For the center of the ball, Construct a sphere with radius At this time, the circle With the ball They intersect at two points, let be the denoted '-'. The local coordinates are The next level of residual height knife site is The two points can be calculated using equation (16). , ,like , with point As the next row of residual height tool positions Otherwise, by point As the next row of residual height tool positions Minimum distance point on the surface That is, a known point Proceed to step 7.2.

[0058] (16)

[0059] Step 7.7: Obtain the desired tool position point with equal residual height. Using the above method, the tool points with equal residual height can be obtained, and the calculated... The coordinates are located at Local coordinates in the unit vector and Substituting into equation (8), we can calculate The global coordinates.

[0060] In the above calculation steps, steps 2-4 are the calculation process for residual height points, and steps 5-7 are the calculation process for tool positions with equal residual height; for the current set of tool positions... The set of tool points with equal residual height in adjacent rows can be obtained by the above steps. By analogy, the calculation of all tool positions with equal residual height can be completed, and finally all tool positions form a complete freeform surface toolpath with equal residual height.

[0061] The beneficial effects of this invention are: compared with the toolpaths calculated by the line spacing adaptive method and the equidistant method, the toolpath generation method for residual height in free-form surface three-axis CNC machining calculated by the method proposed in this invention satisfies the residual height requirements while having the largest line spacing and the smallest total toolpath length. Attached Figure Description

[0062] Figure 1 Flowchart for generating toolpaths with equal residual height;

[0063] Figure 2 For the knife point A schematic diagram of establishing a local coordinate system with the origin;

[0064] Figure 3 This is a schematic diagram for calculating the residual height points;

[0065] Figure 4 A schematic diagram of residual height points for verification, etc.

[0066] Figure 5 Flowchart for calculating residual height points;

[0067] Figure 6 A schematic diagram of establishing a local coordinate system with points of equal residual height as the origin;

[0068] Figure 7 knife point Initial position calculation diagram;

[0069] Figure 8 For discrete feature point set Verification diagram;

[0070] Figure 9 for discrete feature point set Schematic diagram;

[0071] Figure 10 for and discrete feature point set Schematic diagram;

[0072] Figure 11 A schematic diagram for solving the residual tool position points in the next row;

[0073] Figure 12 Flowchart for calculating the knife point with equal residual height;

[0074] Figure 13 This is a schematic diagram of a freeform surface;

[0075] Figure 14 The toolpath with equal residual height generated for this patent;

[0076] Figure 15 Equal spacing toolpaths;

[0077] Figure 16 A schematic diagram showing the row spacing values ​​for toolpaths with equal residual height;

[0078] Figure 17 This is a schematic diagram showing the residual height values ​​of equally spaced toolpaths. Detailed Implementation

[0079] The specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings, but it should be understood that the scope of protection of the present invention is not limited to the specific embodiments.

[0080] Unless otherwise expressly stated, throughout the specification and claims, the term "comprising" or its variations such as "including" or "comprises" shall be understood to include the stated elements or components without excluding other elements or other components.

[0081] To improve the efficiency of CNC machining of freeform surfaces and realize the direct generation of three-axis toolpaths with equal residual height from freeform surface models, this invention provides a method for generating three-axis CNC toolpaths with equal residual height for freeform surface machining, including the following specific steps:

[0082] Step 1: Input the freeform surface model to be machined and the machining parameters, and calculate the set of tool positions for the first pass;

[0083] Let the initial toolpath of the curve be... Let be the curve of the longest side of the freeform surface. Equal-error toolpaths are generated on this curve to obtain the set of tool contact points. The normal vector is calculated for each tool contact point using the k-nearest neighbor method. The set of the first-row tool positions is calculated according to equation (1). ;

[0084] (1)

[0085] Step 2: Construct a local coordinate system at the tool setting point;

[0086] Let the first The set of cutting points is , ,by Create a local coordinate system for the origin. Let vector for The positive direction of the axis, the normal plane is the coordinate plane. , and the global coordinate plane The intersection line as The axis is finally determined using the right-hand rule. Axis; let , , The unit vectors of the axes are respectively , , It can be obtained from equation (2).

[0087] (2)

[0088] any point Coordinates in the local coordinate system It can be obtained from equation (3).

[0089] (3)

[0090] Step 3: Obtain the local free curve segment on the feed direction normal plane;

[0091] Let the plane With freeform surfaces Intersect at curve Because the residual height point is in the line spacing direction, it is in the local coordinate system middle, The value should be within In the positive direction, that is, satisfying ,in correspond in positive direction point , Corresponding to points With center at and radius at, circle Intersection with the curve .

[0092] Step 4: Iteratively calculate the residual height points;

[0093] Step 4.1: Obtain the discrete feature point set on the local free curve segment. Let the parameter region on the curve segment be... , and Each of the interval endpoints is a separate endpoint. and In free curve The parameters on, The number of iterations for this process, its initial discrete number is: That is, at this time, the endpoints of the parameter region correspond to the first point. and the end point The discrete feature point set of the curve segment is obtained by using equation (4). ,in .

[0094] (4)

[0095] Its corresponding point In free curve The parameters can be calculated using equation (5);

[0096] (5)

[0097] for In the interval The position coefficients in the middle are the first and last point coefficients, respectively. , coefficients at intermediate parameter points The coefficients of the two golden ratio points , First discrete feature point set .

[0098] Step 4.2: Obtain the residual height points corresponding to the discrete feature point set; using the discrete feature point set... With each point in the middle as the center, the maximum allowable residual height is... Draw a circle with radius 1. , intersecting the tool circle Assume a set of points. One of the points is Its corresponding residual height point The coordinates are The coordinates of the intersection point are obtained by using equation (6).

[0099] (6)

[0100] For the two calculated intersection points and ,like Then point The residual height points of discrete feature points are added to the point set. Otherwise click The residual height points of discrete feature points are added to the point set. And calculate the point set according to equation (7). The point with the largest value on the horizontal axis is taken as the point with the same residual height. .

[0101] (7)

[0102] Step 4.3: Determine whether the residual height points meet the requirements; based on the residual height points... Centered on the circle, with the maximum allowable residual height as the center, respectively and minimum allowable value Concentric circles with radius Based on the analysis in step 4.2, concentric circles... With free curves Intersecting, with concentric circles There must be one point among the intersection points of the outer circles that lies in the discrete feature point set. In, if and only if concentric circles When the outer circle intersects the free curve and the inner circle separates from the free curve, the residual height point is the target residual height point, and proceed to step 4.4. Otherwise, the requirement for equal residual accuracy is not met, and at this time, the concentric circles... The outer circle intersects the free curve at two points, denoted as and respectively. and Get this time and The coordinates are used, and the curve segment between the two points is taken as the next local free curve region. Returning to step 4.1, if at this point... And because of concentric circles In a circle Internal, therefore it is located inside In the negative direction, therefore the endpoints Calculated as the left endpoint of the iteration region, i.e. .

[0103] Step 4.4: Construct a local coordinate system for the residual height points; the above process can obtain points with equal residual height. The local coordinates of the can be obtained from the global coordinates using equation (8).

[0104] (8)

[0105] Step 5: Construct a local coordinate system for the remaining height points;

[0106] Let the first The set of residual height points is , Similar to step 2, with Create a local coordinate system for the origin. Let vector for The positive direction of the axis, the normal plane is the coordinate plane. , and the global coordinate plane The intersection line as The axis is finally determined using the right-hand rule. Axis, find , , Unit vector of the axis , , , and the coordinates of the point in the local coordinate system;

[0107] Step 6: Set the initial coordinates of the tool position points with equal residual height;

[0108] Step 6.1: Select the region containing the initial value of the tool position point with equal residual height; obtain the plane. Intersection with freeform surface , with residual height points With the center of the circle, Construct a circle with radius . Its satisfaction Due to the tool position point The center of the tool circle is the point through which the tool circle passes. ,and lie in In the positive direction, the tool position point must be located in the circle. an arc on the top Above, that is ,in Represents a circle any point on corresponding and The counterclockwise angle in the positive direction, the endpoint of the region. and Local coordinate systems median coordinate and point.

[0109] Step 6.2: Obtain the region where the initial value of the tool position point is located; it is known that the initial value of the tool position point is located on an arc. Above, its Angle range is And the two endpoints of the arc are and During the first loop , .

[0110] Step 6.3: Obtain the discrete feature point set on the arc region; the discrete feature point set of the arc region is... It can be obtained from equation (9). .

[0111] (9)

[0112] in For the corresponding and The counterclockwise angle in the positive direction can be calculated using equation (10).

[0113] (10)

[0114] for In the interval The position coefficients in the middle are the coefficients of the first and last points, respectively. , The coefficients of the midpoint parameter points The coefficients of the two golden ratio points , .

[0115] Step 6.4: Determine whether the points in the discrete feature point set meet the accuracy requirements; in the point set... middle, and The two corresponding points are boundary points, which in the iteration process are the points in the previous loop and the curve, respectively. The centers of the tool circles that are completely intersecting and completely disjoint are not included in the calculation during the iteration process; only the centers are discussed. ,from Start in sequence, with Centered on the circle, with the tool radius as the center, respectively and precision radius For radius, Draw a concentric tool circle given the user's radius accuracy. until satisfied concentric cutting tool circle Inner and outer circles and curves Separated. At this time, and As the arc region in the next iteration The boundary points are re-recorded as points. and Proceed to step 6.2. Record the concentric tool circle. Outer circle and curve If the inner circle of the two objects intersects but the inner circle of the two objects is not to each other, then they can be considered tangent, which satisfies the accuracy requirements and obtains the initial value of the desired equal residual height tool position. Its corresponding tangent point is If concentric circles at this time Outer circle and curve Intersect at two points and tangent point for perpendicular bisector and free curve of the line The intersection point.

[0116] Step 7: Iteratively calculate the knife point with equal residual height;

[0117] Step 7.1: Obtain the initial tool position point and known points on intersecting surfaces Assuming the tool is at the initial tool position... The point intersects with the freeform surface. According to Section 2.1, there exists a known point on the intersecting surface. That is, the tangent point .

[0118] Step 7.2: Obtain the initial discrete directions of known points on the intersecting surfaces. ; Obtain known points on the intersecting surfaces according to equation (11) of , parameter and In the parameter direction respectively , , and Increase parameter increment Four new points can be obtained by calculating using equations (11) and (12);

[0119] (11)

[0120] (12)

[0121] according to , , and Directional order constitutes a point set , The degree of local surface discretization. Calculate the point set The set of distances from each point in the middle to the tool's cutting point The minimum distance is Calculated by equation (13);

[0122] (13)

[0123] Its corresponding point Let it be the point of minimum distance. Initial discrete direction Based on the minimum distance point correspond The value is obtained by taking the minimum distance point at this time. Corresponding Then the initial discrete order Initial discrete direction for Direction, otherwise At that time, the initial discrete order Initial discrete direction for direction.

[0124] Step 7.3, for Discretize feature points along the parameter direction; because for Feature points are discretized along the parameter direction, hence the number of discretization operations. Assuming at this time... Parameter direction is Parameter direction, and passes through the minimum distance point The curve intersects the boundary of the intersecting surface at... and The curve segment is obtained by calculating according to equation (11). The corresponding new parameter area is The point with the smallest distance At the initial discrete time, it is According to equation (14), the parameter region Discretize the feature points;

[0125] (14)

[0126] Its point set is , ,in For point The parameters on the tool contact point trajectory line can be calculated using equation (15);

[0127] (15)

[0128] for In the interval The position coefficients in the middle are the coefficients of the first and last points, respectively. , The coefficients of the three quadrature parameter points , , The coefficients of the two golden ratio points , And calculate the discrete feature point set. From each feature point to the tool's cutting point Distance between The minimum distance is calculated according to equation (13) as follows: The minimum distance point is ,like Parameter direction is Parameter direction, and The calculation process for the parameter direction is the same.

[0129] Step 7.4: Determine the point of minimum distance Does the accuracy meet the requirements? and When, then the minimum distance point This can be denoted as the point of minimum distance from the intersecting surfaces to the tool point. The minimum distance is Otherwise, minimum distance point The accuracy does not meet the requirements; assume discrete direction. and discrete degree Correlation, when discrete order When the number is odd, the discrete direction is Direction, or conversely, discrete order When the number is even, the discrete direction is then... Direction. Then, based on the discrete order... Regain Discrete Direction Return to step 7.3.

[0130] Step 7.5: Determine the point of minimum distance on the surface. Does the residual accuracy meet the requirements? If the minimum distance point on the curved surface meets the residual height accuracy requirements, that is... This indicates that the tool position point with the same residual height is the same as the target tool position point with the same residual height. Proceed to step 7.7. Otherwise, if the minimum distance point does not meet the residual accuracy requirements, continue the iteration.

[0131] Step 7.6: Based on the minimum distance point on the surface Regain the same residual height tool position To facilitate calculations, a local coordinate system is selected. First of all On the plane, based on the residual height point With the center of the circle, Draw a circle with radius 1. At the same time, at the point of minimum distance For the center of the ball, Construct a sphere with radius At this time, the circle With the ball They intersect at two points, let be the denoted '-'. The local coordinates are The next level of residual height knife site is The two points can be calculated using equation (16). , ,like , with point As the next row of residual height tool positions Otherwise, by point As the next row of residual height tool positions Minimum distance point on the surface That is, a known point Proceed to step 7.2.

[0132] (16)

[0133] Step 7.7: Obtain the desired tool position point with equal residual height. Using the above method, the tool points with equal residual height can be obtained, and the calculated... The coordinates are located at Local coordinates in the unit vector and Substituting into equation (8), we can calculate The global coordinates.

[0134] In the above calculation steps, steps 2-4 are the calculation process for residual height points, and steps 5-7 are the calculation process for tool positions with equal residual height; for the current set of tool positions... The set of tool points with equal residual height in adjacent rows can be obtained by the above steps. By analogy, the calculation of all tool positions with equal residual height can be completed, and finally all tool positions form a complete freeform surface toolpath with equal residual height.

[0135] A typical embodiment of the present invention is as follows: the selected example is a typical freeform surface, such as... Figure 13 As shown, the dimensions of the enclosure box are 130mm×130mm×105mm, the cutting tool selected is a ball end mill with a diameter of 12mm, and the maximum allowable residual height is 0.2mm. Figure 14 The toolpath with constant residual height generated by this invention Figure 15 The toolpaths are of equal spacing, with 43, 47, and 50 toolpath rows respectively. Figure 16 The line spacing value of 8 lines of toolpaths with equal residual height. Figure 17The residual height values ​​are for 8 rows of equally spaced toolpaths. All toolpath information is shown in Table 1. The maximum residual height of the 50-row equally spaced toolpath is 0.208 mm, with only the residual height of the first row exceeding the maximum allowable value of 0.2 mm. The residual height range of the equally spaced toolpath calculated by this invention is [0.180, 0.199], which meets the requirements. Furthermore, it reduces the number of rows by 14% and the total length by 17.1% compared to the 50-row equally spaced toolpath, verifying the feasibility and effectiveness of the algorithm.

[0136] Table 1 Toolpath Information

[0137]

[0138] In summary, this invention provides a method for generating toolpaths with equal residual height in three-axis CNC machining of free-form surfaces. By directly generating residual height points on the free-form surface, and to improve computational efficiency, an adaptive discretization method is proposed. This method uses a set of discrete feature points, including the golden section point, to reduce the number of discretization iterations, thereby iteratively obtaining the residual height points. To further improve computational efficiency, a new method for calculating the initial tool position point is proposed, and the adaptive discretization method is used again to obtain the minimum distance point from the intersecting surface to the tool position point, thus obtaining the target tool position point with equal residual height. Finally, the equal residual toolpath is generated. Compared with toolpaths calculated by the line spacing adaptive method and the equidistant method, the equal residual height toolpath for three-axis CNC machining of free-form surfaces calculated using the method proposed in this invention satisfies the residual height requirement while having the smallest number of toolpath rows and the smallest total toolpath length.

[0139] The above description is merely an embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent structural or procedural transformations made based on the content of the present invention specification, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of the present invention.

Claims

1. A method for generating a residual height equalization tool path for free-form surface three-axis NC machining, characterized in that, The method comprises the following specific steps: Step 1, inputting a free surface model to be processed and processing parameters, and calculating a first row of tool position point set; Let the initial tool path of the curve be , the longest side of the free-form surface curve, and the equal error tool path is generated, and then the tool contact point set is obtained , the normal vector of each tool contact point is calculated by using the k-neighbor method , the first row of tool position point set is calculated according to formula (1) ; (1) Step 2, constructing a local coordinate system for the tool position point; Let the set of cutting sites be , , , , , , , , , , , , , , , , , (2) (2) arbitrary point coordinates in local coordinate system may be obtained from equation (3); (3) Step 3, obtaining a local free curve segment on a feed direction normal plane; Let plane With freeform surfaces Intersect at curve Because the residual height point is in the line spacing direction, it is in the local coordinate system middle, The value should be within In the positive direction, that is, satisfying ,in correspond in positive direction point , Corresponding to points With center at and radius at, circle Intersection with the curve ; Step 4, iteratively calculating a residual height point; Step 4.1, obtaining the discrete feature point set on the local free curve segment; let the parameter region on the curve segment be , and be the interval end points and on the free curve , be the parameter, be the iteration number of this process, and the initial discrete number be , that is, the end point pair corresponding to the initial point and the terminal point at this time, the discrete feature point set of the curve segment is obtained by using formula (4) , wherein ; (4) for its corresponding point In free curve The parameter, which can be calculated by equation (5); (5) For The position coefficients in the interval are respectively the first and last point coefficients , the coefficient of the intermediate parameter point , the coefficient of the two golden section points , , the first discrete feature point set ; Step 4.2, obtaining the residual height point corresponding to the discrete feature point set; taking each point in the discrete feature point set as a circle center and a maximum allowed value of the residual height as a radius to draw a circle , the coordinates of the residual height point corresponding to the point are calculated by using formula (6) to obtain the intersection point coordinates​​​​​​​ (6) For the two intersection points calculated and , if , then the point is added to the point set as a residual height point of the discrete feature point , otherwise the point is added to the point set as a residual height point of the discrete feature point , and the point with the largest horizontal coordinate in the point set is calculated as the equal residual height point according to formula (7) ; (7) Step 4.3, judging whether the equal residual height point meets the requirement; taking the equal residual height point as the center to draw concentric circles with the maximum allowed value of residual height and the minimum allowed value of residual height as the radii, respectively ; Based on the analysis in step 4.2, concentric circles were obtained. With free curves Intersecting, with concentric circles There must be one point among the intersection points of the outer circles that lies in the discrete feature point set. In, if and only if concentric circles When the outer circle intersects the free curve and the inner circle separates from the free curve, the residual height point is the target residual height point, and proceed to step 4.

4. Otherwise, the requirement for equal residual accuracy is not met, and at this time, the concentric circles... The outer circle intersects the free curve at two points, denoted as and respectively. and ; acquire the coordinates of this time and the curve segment between two points as the next local free curve region Return to step 4.1, if one of the points at this time , and since the concentric circle is inside the circle , it is in the negative direction of , so the end point is calculated as the left end point of the iteration region, that is ; Step 4.4, construct local coordinate system for residual height points; the above procedure can obtain equal residual height points with local coordinates, whose global coordinates can be obtained by equation (8); (8) Step 5, constructing a local coordinate system for the residual height point; Set the first line residual height point set as , , create a local coordinate system with the origin , let the vector be the positive direction of the axis, and the normal plane is the coordinate plane , the intersection of the global coordinate plane as the axis , and finally determine the axis with the right-hand rule, find the unit vectors of the axes , , , and the coordinates of the points in the local coordinate system , , , and , . Step 6, setting a coordinate initial value of the tool position point with equal residual height; Step 6.1: Select the region containing the initial value of the tool position point with equal residual height; obtain the plane. Intersection with freeform surface , with residual height points With the center of the circle, Construct a circle with radius . Its satisfaction Due to the tool position point The center of the tool circle is the point through which the tool circle passes. ,and lie in In the positive direction, the tool position point must be located in the circle. an arc on the top Above, that is ,in Represents a circle any point on corresponding and The counterclockwise angle in the positive direction, the endpoint of the region. and Local coordinate systems median coordinate and point; Step 6.2, obtaining a region where the tool position point initial value is located; The initial value of the tool position is located on a circular arc The initial value of the tool position is located on a circular arc The initial value of the tool position is located on a circular arc The initial value of the tool position is located on a circular arc The initial value of the tool position is located on a circular arc The initial value of the tool position is located on a circular arc The initial value of the tool position is located on a circular arc The initial value of the tool position is located on a circular arc Step 6.3, obtaining a discrete feature point set on the circular arc region; the discrete feature point set of the circular arc region is may be obtained from equation (9), ; (9) wherein corresponding to with the clockwise angle of the positive direction, which can be calculated by equation (10); (10) For the position coefficient in the interval , the coefficients of the first and last points respectively , the coefficient of the midpoint parameter point , the coefficients of the two golden section points , ; Step 6.4: Determine whether the points in the discrete feature point set meet the accuracy requirements; in the point set... middle, and The two corresponding points are boundary points, which in the iteration process are the points in the previous loop and the curve, respectively. The centers of the tool circles that are completely intersecting and completely disjoint are not included in the calculation during the iteration process; only the centers are discussed. ,from Start in sequence, with Centered on the radius of the cutting tool, respectively and precision radius For radius, Draw a concentric tool circle given the user's radius accuracy. until satisfied concentric cutting tool circle Inner and outer circles and curves Separated; at this time and As the arc region in the next iteration The boundary points are re-recorded as points. and Proceed to step 6.2; record the concentric tool circle. Outer circle and curve If the inner circle of the two objects intersects but the inner circle of the two objects is not to each other, then they can be considered tangent, which satisfies the accuracy requirements and obtains the initial value of the desired equal residual height tool position. Its corresponding tangent point is If concentric circles at this time Outer circle and curve Intersect at two points and tangent point for perpendicular bisector and free curve of the line The intersection; Step 7, iteratively calculating the tool position point with equal residual height; Step 7.1, obtaining initial knife point and known points on intersecting surfaces ; Assume that the tool intersects with the free-form surface at the initial tool position According to the content of section 2.1, there is a known point on the intersection surface , which is the tangent point . Step 7.2, obtaining initial discrete directions of known points on the intersection surface ; obtaining the parameters u and v of the known point on the intersection surface according to formula (11) , parameters and , respectively, add parameter increments , , and to the parameter directions , four new points can be calculated according to formula (11) and (12);​ (11) (12) In , , and directional order to form a point set , is the local surface discrete number, , the distance set of each point in the point set to the tool position point is calculated , wherein the minimum distance is obtained by formula (13); (13) its corresponding point is called the minimum distance point , initial discrete direction According to the minimum distance point , the value of the corresponding is obtained, if the minimum distance point corresponds to at this time, the initial discrete number , the initial discrete direction is direction, otherwise , the initial discrete number , the initial discrete direction is direction; Step 7.3, the feature points are dispersed in the parameter direction; because the feature points are dispersed in the parameter direction, the dispersion times ; because the feature points are dispersed in the parameter direction, the dispersion times ; because the feature points are dispersed in the parameter direction, the dispersion times ; suppose that at this time ; because the feature points are dispersed in the parameter direction, the dispersion times ; because the feature points are dispersed in the parameter direction, the dispersion times ; the curve passing through the minimum distance point and the boundary of the intersecting surface intersects at and , the curve segment corresponding to the new parameter region is obtained according to formula (11); wherein the minimum distance point is at the initial dispersion, and the feature points are dispersed in the parameter region according to formula (14). (14) The point set is , wherein is the point The parameter on the tool contact point trajectory line can be obtained by formula (15); (15) For The position coefficient in the interval The coefficients of the first and last points, respectively , The coefficients of the three fourth division parameter points , , The coefficients of the two golden section points , And calculate the distance between each feature point in the discrete feature point set And the tool position point The minimum distance is , calculated according to formula (13) , and the minimum distance point is , if The parameter direction is The parameter direction, and The parameter direction calculation process is consistent. Step 7.4, judging whether the minimum distance point satisfies the requirement of accuracy; if and , then the minimum distance point can be recorded as the minimum distance point of the intersection surface to the tool position point at this time , the minimum distance is , otherwise the minimum distance point does not satisfy the requirement of accuracy, assuming that the discrete direction and the discrete number are related, when the discrete number is odd, the discrete direction is the direction, otherwise the discrete number is even, the discrete direction is the direction, then the discrete direction is obtained again according to the discrete number , and the step 7.3 is returned. Step 7.5, judging the minimum distance point of the curved surface whether the residual accuracy meets the requirements; if the minimum distance point of the curved surface meets the residual height accuracy requirements, that is, , it indicates that the equal residual height tool position at this time is the target equal residual height tool position, and the step 7.7 is transferred, otherwise the minimum distance point does not meet the residual accuracy requirements, and the iteration is continued. Step 7.6: Based on the minimum distance point on the surface Regain the same residual height tool position To facilitate calculations, a local coordinate system is selected. First of all On the plane, based on the residual height point With the center of the circle, Draw a circle with radius 1. At the same time, with the minimum distance point For the center of the ball, Construct a sphere with radius 1 At this time, the circle With the ball They intersect at two points, let be the denoted '-'. The local coordinates are The next level of residual height knife site is The two points can be calculated using equation (16). , ,like , with point As the next row of residual height tool positions Otherwise, by point As the next row of residual height tool positions Minimum distance point on the surface That is, a known point Proceed to step 7.2; (16) Step 7.7, Obtain the desired equal residual height tool position ; The equal residual height tool position is obtained by the above method, the calculated coordinates are local coordinates in the , the unit vectors and are substituted into equation (8) to calculate the global coordinates of ; In the above calculation steps, steps 2-4 are the residual height point calculation process, and steps 5-7 are the equal residual height tool position calculation process; the current row tool position set The adjacent row equal residual height tool position set can be obtained by the above steps By analogy, the calculation of all row equal residual height tool positions can be completed, and finally all tool positions form a complete equal residual height tool path of the free-form surface.

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