阅读说明：本技术 一种基于数控插补映射的曲面参数域自适应划分方法 (Curved surface parameter domain self-adaptive partitioning method based on numerical control interpolation mapping ) 是由 孙扬帆 于 2021-09-13 设计创作，主要内容包括：本发明公开了一种基于数控插补映射的曲面参数域自适应划分方法,该方法能实现机床动态特性在曲面参数域上的映射,实现曲面区域的划分。针对输入的待加工曲面,该方法先在参数域等参数生成一组网格,在网格单元的参考点上比较机床各轴的变化状态,以此为依据为网格标记标签。通过聚合算法将同标签的相连网格汇聚成区域,最后通过链式算法获取区域边界轮廓。划分结果能保证在相同区域内以相同策略规划的刀路能最大程度的发挥机床动态特性,满足高速、高精度加工的要求。(The invention discloses a curved surface parameter domain self-adaptive dividing method based on numerical control interpolation mapping, which can realize the mapping of the dynamic characteristics of a machine tool on a curved surface parameter domain and realize the division of a curved surface region. Aiming at the input curved surface to be processed, the method firstly generates a group of grids in a parameter domain and other parameters, compares the change state of each axis of the machine tool on the reference point of a grid unit, and marks labels on the grids according to the change state. And aggregating connected grids with the labels into a region through an aggregation algorithm, and finally acquiring a region boundary outline through a chain algorithm. The division result can ensure that the cutter paths planned by the same strategy in the same region can exert the dynamic characteristics of the machine tool to the maximum extent, and meet the requirements of high-speed and high-precision machining.)

1. A curved surface parameter domain self-adaptive dividing method based on numerical control interpolation mapping is characterized by comprising the following steps:

(1) inputting Surf (u, v) of the curved surface to be processed, a reverse kinematics model of the machine tool and dynamic parameters of each axis of the machine tool, wherein u and v are parameter domain directions of the Surf (u, v) of the curved surface to be processed.

(2) Generating equal interval parameter mesh in curved surface parameter domainIs recorded as

(3) Calculating the grid cells of the tool in the ith row and the j column according to the inverse kinematics model of the machine toolReference pointPosition of each axis of the machine toolWherein x is a reference point of the grid unit on each parameter line, and x ═ u_i，u_i+1，v_j，v_j+1}; ) (ii) a The machine tool inverse kinematics model is a inverse kinematics relation which converts the track of the machine tool moving cutter terminal into the displacement of each axis of the machine tool and is determined by a machine tool motion chain, and the track of the machine tool moving cutter terminal is determined by a cutter reference point coordinate Surf_ij，x＝[x，y，z]And tool axis vector T_ii，x＝[T_x，T_y，T_z]And (4) forming.

(4) And calculating the values of each dynamic channel of the grid.

(5) And respectively calculating the feed speed channel values of different feed directions.

(6) Comparing feeding of grid cells moving in different directionsThe speed is high or low, the grid cells are marked with labels, the grid cells are traversed until all the cells are marked, and the grids with the labels are marked

(7) Aggregating connected grids with the same label into areas; note region as Z_i(i ═ 1,2, 3.. k), then

(8) And extracting edge mesh units of the region, sequentially connecting and generating region outlines, and realizing the self-adaptive division of the curved surface parameter domain.

2. The method of claim 1, wherein in step 1, the machine tool axis dynamics parameters include a speed limit value V_kmaxAcceleration limit value of A_kmaxJerk limit of J_kmax. (ii) a k is X, Y, Z, a or C, and represents X, Y, Z, A or C axis.

3. The method according to claim 1, wherein the step 2 is specifically: generating n multiplied by n isoparametric grids by adopting isoparametric lines along u and v directions of a parameter domain, and recording the grids asEach grid has four reference points, which are the midpoints of the edges of the grid.

4. The method of claim 1, wherein said step 3 comprises the sub-steps of:

(3.1) at the reference pointAt the time of cutting tool position isNamely the coordinate of the center point of the cutter, namely the coordinate of the grid reference point;

(3.2) recording grid reference pointsThen Surf_ij，x＝S(u_ij，x，v_ij，x)。T_ij，xThe local geometric property of the curved surface is determined by the curved surface space point corresponding to the grid reference point, and the curved surface S is formed by the local geometric property of the curved surface_ij，xIs provided with a two-parameter unitary frameCutter axis vector T_ij，xDefined in a frameIn (1). According to the reverse kinematic model of the machine tool, the tool is on the curved surface S_ij，xThe position and posture angle [ S ]_ij，x，T_ij，x]Can be decomposed into actual positions [ X ] of the axes_ij，x，Y_ij，x，Z_ij，x，A_ij，x，C_ij，x]Is marked as

5. The method of claim 1, wherein said step 4 comprises the sub-steps of:

(4.1) calculating the speed channel value of the grid unit when moving along the u directionAt each axis of a velocity channel value ofSimilarly, when moving in the v directionAt a speed of each axis ofThereby obtaining a grid velocity channel value.

(4.2) according to the grid speed channel value, obtaining a grid acceleration channel value, wherein the u direction:definition ofFurther, the jerk channel value isDefinition ofv direction:definition ofFurther, the jerk channel value isDefinition of

6. The method of claim 1, wherein the step 5 is to convert the velocity channel value, the acceleration channel value and the jerk channel value on each grid into the feed velocity channel value according to a velocity planning model satisfying the machine tool dynamics constraints, and taking u-direction calculation as an example, the i-th grid, the j-th grid, has a progress velocity along the u-direction as follows:wherein:

similarly, the speed of the progress of the grids in the ith row and the j column along the v direction is as follows:wherein:

7. the method according to claim 1, wherein in step 6, comparing the feeding speed of the grid unit moving in different directions, and marking the grid unit with the label specifically comprises: recording the reference point of the tool in the same grid along the u direction And recording position attributes at each reference point according to the position of each axis of the machine tool, calculating a speed attribute, an acceleration attribute and an acceleration attribute unit by unit, finally calculating the feeding speed on the reference point, marking the grid as a U-type grid if the speed in the U direction is greater than the speed in the V direction, and otherwise marking the grid as a V-type grid. If both speeds are lower, the grid is marked as an O type grid.

8. The method of claim 1, wherein in step 7, the grids include 3 types, namely, attribute-bearing grids, attribute-free grids, and edge grids. The method comprises the following steps:

(7.1) selecting a gridAnd, any area-attributed grid cells not yet attributedMarking as a seed grid cell and willAdding to a set of regions

(7.2) meshing the cellsAdding surrounding co-tagged attribute grids to auxiliary definition spacePerforming the following steps;

(7.3) in the definition spaceIn selecting arbitrary grid cellsPut into a set of regions for a seed unitIn and (2) mixingDefining a space from an auxiliaryDeleting;

(7.4) ifDefining a spaceIf not, repeating the steps (1) to (3);

(7.5) if a space is definedEmpty, end the aggregation process, region aggregationNamely the seed gridThe region to which the cell belongs;

(7.6) all independent areas of the parameter domain are in turn available.

9. The method of claim 1, wherein said step 8 comprises the steps of:

(8.1) defining edge units, and collecting the regionsPutting any edge unit into the contour set and defining the edge unit as a seed unit;

(8.2) traversing adjacent units of the seed unit, adding edge units which do not belong to the outline set into the temporary set, and if only one unit exists in the temporary set, putting the unit into the outline set and setting the unit as a new seed unit;

(8.3) if more than one unit in the temporary set is available, selecting the unit closest to the temporary set as a new seed unit;

and (8.4) if the temporary set is empty, ending traversal and finishing the generation of the sub-region outline.

Technical Field

The invention relates to the field of five-axis tool path planning, in particular to a self-adaptive tool path generation method considering the dynamic characteristics of a five-axis machine tool.

Background

The complex curved surface parts have irreplaceable significance in the industries of military industry, molds, aerospace aviation and the like, and the manufacturing level of the complex curved surface parts is the embodiment of national advanced manufacturing capability. The machining of the complex curved surface generally adopts a five-axis numerical control machine tool, and compared with a three-axis machine tool, the two additional rotating shafts of the five-axis machine tool can control the attitude angle of a cutter when a machining path is swept, so that the interference between the cutter and the curved surface is avoided, and the machinability of the machine tool is greatly improved. However, machine dynamics can affect the kinematic performance of the axes, for example, in order to allow the tool to rotate relative to the X-axis (i.e., the a-axis), the axis of rotation is typically mounted on a table that rotates the workpiece. Due to the large rotational inertia of the table, frequent acceleration and deceleration of the a-axis can cause the a-axis drive to flutter, which in turn has to reduce the overall feed rate. Unreasonable tool path planning can cause the numerical control interpolation to fail to exert the maximum performance of the machine tool, and the tool is usually the main reason for clamping the feeding speed due to the excessively fast change of the pose of the tool in some feeding directions. In the traditional five-axis machining path planning process, only the geometric characteristics of the curved surface are generally considered, and a uniform path planning strategy is adopted in the whole curved surface. However, the sensitive direction of the tool pose change is constrained by the local geometric characteristics of the curved surface, and the distribution of the local geometric characteristics of the curved surface is determined by the characteristics of the part, so that certain irregularity exists. Therefore, it is difficult to ensure that the generated five-axis tool path conforms to the dynamic characteristics of the machine tool by adopting the same path planning strategy in the curved surface.

In the existing five-axis tool path planning literature, a curved surface self-adaptive dividing method based on a numerical control interpolation result is not available. In the literature, some scholars have provided some exploration for the division of curved surface areas and achieved some results: elber proposes dividing a curved surface into three typical regions according to the curvature of the curved surface^[1](ii) a Roman discretizes curved surfaces into point clouds by sampling^[2]Automatically dividing the point cloud into similar point cloud clusters through a Fuzzy C-means algorithm; ding proposes dividing a curved surface into different regions using an equal illumination method. The existing curved surface dividing method is to directly divide the three-dimensional curved surface to obtain the area based on the local geometric property of the curved surface^[3]Or dispersing the curved surface into a plurality of sampling points through the sampling points, and then adopting a mean value clustering algorithm to realize region division on the sampling points with similar geometric properties. The method can only realize the curved surface division based on the geometric characteristics, but the curved surface division considering the numerical control interpolation result cannot be realized.

According to the above literature analysis, the conventional curved surface dividing method is only suitable for dividing based on the geometric characteristics of the curved surface, and there is no curved surface dividing method suitable for taking the interpolation information of the machine tool into consideration.

Disclosure of Invention

The invention aims to provide a curved surface parameter domain self-adaptive dividing method based on numerical control interpolation information mapping, aiming at the defects of the prior art, and the method can realize the mapping of the dynamic characteristics of a machine tool on a curved surface parameter domain and realize the division of a curved surface region.

The purpose of the invention is realized by the following technical scheme: a curved surface parameter domain self-adaptive dividing method based on numerical control interpolation mapping comprises the following steps:

(1) inputting Surf (u, v) of the curved surface to be processed, a reverse kinematics model of the machine tool and dynamic parameters of each axis of the machine tool, wherein u and v are parameter domain directions of the Surf (u, v) of the curved surface to be processed.

(2) Generating equal interval parameter mesh in curved surface parameter domainIs recorded as

(3) Calculating the grid cells of the tool in the ith row and the j column according to the inverse kinematics model of the machine toolReference pointPosition of each axis of the machine toolWherein x is a reference point of the grid unit on each parameter line, and x ═ u_i,u_i+1,v_j,v_j+1}; ) (ii) a The machine tool inverse kinematics model is a inverse kinematics relation which converts the track of a machine tool moving cutter terminal into the displacement of each axis of the machine tool and is determined by a machine tool kinematic chain, and the track of the machine tool moving cutter terminal is determined by a cutter reference point coordinate surf_ij,x＝[x,y,z]And tool axis vector T_ij,x＝[T_x,T_y,T_z]And (4) forming.

(4) And calculating the values of each dynamic channel of the grid.

(5) And respectively calculating the feed speed channel values of different feed directions.

(6) Comparing grid sheetsThe feeding speed of the elements moving along different directions marks labels for the grid cells, and the grid cells are traversed until all the cells are marked, and the grids with the labels are marked

(7) Aggregating connected grids with the same label into areas; note region as Z_i(i is 1,2,3 … k), then

(8) And extracting edge mesh units of the region, sequentially connecting and generating region outlines, and realizing the self-adaptive division of the curved surface parameter domain.

Further, the dynamic parameters of each shaft of the machine tool comprise a speed limit value V_kmaxAcceleration limit value of A_kmaxJerk limit of J_kmax. (ii) a k is X, Y, Z, a or C, and represents X, Y, Z, A or C axis.

Further, the step 2 specifically includes: generating n multiplied by n isoparametric grids by adopting isoparametric lines along u and v directions of a parameter domain, and recording the grids asEach grid is provided with four reference points which are respectively the middle points of each side of the grid;

further, the step 3 comprises the following substeps:

(3.1) at the reference pointAt the time of cutting tool position isNamely the coordinate of the center point of the cutter, namely the coordinate of the grid reference point;

(3.2) recording grid reference pointsThen Surf_ij,x＝S(u_ij,x,v_ij,x)。T_ij,xThe local geometric property of the curved surface is determined by the curved surface space point corresponding to the grid reference point, and the curved surface S is formed by the local geometric property of the curved surface_ij,xIs provided with a two-parameter unitary frameCutter axis vector T_ij,xDefined in a frameIn (1). According to the reverse kinematic model of the machine tool, the tool is on the curved surface S_ij,xThe position and posture angle [ S ]_ij,x,T_ij,x]Can be decomposed into actual positions [ X ] of the axes_ij,x,Y_ij,x,Z_ij,x,A_ij,x,C_ij,x]Is marked as

Further, the step 4 comprises the following substeps:

(4.1) calculating the speed channel value of the grid unit when moving along the u directionAt each axis of a velocity channel value ofSimilarly, when moving in the v directionAt a speed of each axis ofThereby obtaining a grid velocity channel value.

(4.2) according to the grid speed channel value, obtaining a grid acceleration channel value, wherein the u direction:definition ofFurther, the jerk channel value isDefinition of v direction:definition ofFurther, the jerk channel value isDefinition of

Further, in step 5, the speed channel value, the acceleration channel value, and the jerk channel value on each grid may be converted into a feed speed channel value according to a speed planning model satisfying the machine tool dynamics constraint, where, taking u-direction calculation as an example, the progress speed along u-direction of the ith row and j column grid is:wherein:

similarly, the speed of the progress of the grids in the ith row and the j column along the v direction is as follows:wherein:

further, in step 6, the comparing the feeding speed of the grid unit moving along different directions includes: recording the reference point of the tool in the same grid along the u directionAnd recording position attributes at each reference point according to the position of each axis of the machine tool, calculating a speed attribute, an acceleration attribute and an acceleration attribute unit by unit, finally calculating the feeding speed on the reference point, marking the grid as a U-type grid if the speed in the U direction is greater than the speed in the V direction, and otherwise marking the grid as a V-type grid. If both speeds are lower, the grid is marked as an O type grid.

Further, in step 7, the grids include 3 types, namely, a grid with attribute, a grid without attribute, and an edge grid. The method comprises the following steps:

(7.1) selecting a gridIn the arbitrary area with attribute grid cell not belonging toMarking as a seed grid cell and willAdding to a set of regions

(7.2) meshing the cellsSurrounding homotagged attribute gridAdding to auxiliary definition spacePerforming the following steps;

(7.3) in the definition spaceIn selecting arbitrary grid cellsPut into a set of regions for a seed unitIn and (2) mixingDefining a space from an auxiliaryDeleting;

(7.4) if a space is definedIf not, repeating the steps (1) to (3);

(7.5) if a space is definedEmpty, end the aggregation process, region aggregationNamely the seed gridThe region to which the cell belongs;

(7.6) all independent areas of the parameter domain are in turn available.

Further, the step 8 comprises the following steps:

(8.1) defining edge units, and collecting the regionsPutting any edge unit into the contour set and defining the edge unit as a seed unit;

(8.2) traversing adjacent units of the seed unit, adding edge units which do not belong to the outline set into the temporary set, and if only one unit exists in the temporary set, putting the unit into the outline set and setting the unit as a new seed unit;

(8.3) if more than one unit in the temporary set is available, selecting the unit closest to the temporary set as a new seed unit;

and (8.4) if the temporary set is empty, ending traversal and finishing the generation of the sub-region outline.

The method has the advantages that the mapping of the dynamic characteristics of the machine tool on the curved surface parameter domain can be realized, and the division of the curved surface area is realized. Aiming at the input curved surface to be processed, the method generates a group of grids according to the parameters such as the current parameter domain, compares the change state of each axis of the machine tool on the reference point of the grid unit, and marks labels on the grids according to the change state. And aggregating connected grids with the labels into a region through an aggregation algorithm, and finally acquiring a region boundary outline through a chain algorithm. The division result can ensure that the cutter paths planned by the same strategy in the same region can exert the dynamic characteristics of the machine tool to the maximum extent, and meet the requirements of high-speed and high-precision machining.

Drawings

FIG. 1 is a flow chart of the adaptive partitioning of a mesh in accordance with the present invention;

FIG. 2 is an effect diagram of surface generation isoparametric mesh;

FIG. 3 is a schematic diagram of grid unit tool reference points and tool poses corresponding to the grid unit tool reference points on a curved surface, wherein (a) is a grid v-direction reference point, (b) is a grid v-direction reference point tool pose, (c) is a grid u-direction reference point, and (d) is a grid u-direction reference point tool pose;

FIG. 4 is a schematic diagram of grid reference point calculation;

FIG. 5 is a schematic diagram of calculation of pose change of grid tool, wherein (a) is a schematic diagram of tool feeding direction, and (b) is a schematic diagram of tool pose channel value, and

FIG. 6 is a schematic diagram of the grid corresponding to the channel values of the machine tool axes;

FIG. 7 is a graph of grid velocity channel values;

FIG. 8 is a graph illustrating grid acceleration channel values;

FIG. 9 is a graph illustrating grid jerk channel values;

FIG. 10 is a diagram illustrating the conversion of each channel of the grid into an attribute;

fig. 11 is a schematic diagram of mesh aggregation.

Detailed Description

In order to more specifically describe the present invention, the following detailed description is provided for the technical solution of the present invention with reference to the accompanying drawings and the specific embodiments.

As shown in FIG. 1, the method for adaptively dividing the parameter domain of the curved surface based on the numerical control pre-interpolation mapping comprises the following specific steps:

step 101: inputting Surf (u, v) of a curved surface to be processed, a reverse kinematics model of a machine tool and dynamic parameters of each axis of the machine tool;

in the step, the curved surface Surf (u, v) is obtained by modeling any mainstream commercial software and is stored in an iges file in a NURBS curved surface form; wherein u and v are two parameters and are subjected to standardization treatment, namely u, v epsilon [0,1 ].

In this step, the machine tool is not limited by the type of the machine tool, and may be a double rotary table type (RT) five-axis numerical control machine tool or a spindle rotary type (SR) five-axis numerical control machine tool. The machine tool kinematic chain is determined by the machine tool structure.

In the step, the dynamic parameters of each axis of the machine tool are determined by the structure of the machine tool and the characteristics of parts, and can be measured by referring to the specification of the machine tool or experiments.

Step 102: the elementary grid cells are generated by an isoparametric method, and the rays parallel to the coordinate axes of the parameter domain are used as boundaries and intersect to form elementary grids with equal sizes, as shown in fig. 2.

Step 103: the center point of each edge of the grid is the reference point of the grid unit, each axial displacement along the u direction corresponds to the displacement of each axis when the calculation tool sequentially passes through the center points of the two v lines, and similarly, each axial displacement along the v direction corresponds to the displacement of each axis when the calculation tool sequentially passes through the center points of the two u lines, as shown in fig. 3.

Step 104: the attribute values of each channel of the grid are calculated according to a speed planning model meeting the dynamics of the machine tool, and the analytical expression of the model is as follows:

wherein Q(s) ([ X(s), Y(s), Z(s), A(s), C (s))]Is the position vector of the machine tool in the current state, s is the arc length parameter of the cutter feeding curve,the arc length parameter is obtained by one derivation relative to the time t, and similarly,the second and third derivation of the arc length to the time t. The velocity value, acceleration value and jerk value may be approximated and replaced by forward differences of grid reference points to obtain the dynamic channel values of the grid, the principle of which is shown in fig. 4.

Step 105: from the channel values, it can be calculated that the feeding speed feasible region in the current state of the machine tool can be expressed as (i.e. as shown in fig. 7-9):

step 106: respectively calculating the feed speed feasible threshold values of the machine tool in the specified grid in the u direction feed and the v direction feed, if the grid unit isF is treated_i,j,u>f_i,j,vThen defineIs a U-type grid; on the contrary, if f_i,j,u<f_i,j,vThe label is a V-type grid. If both speeds are less than f_minThen the grid is marked as an O type grid as shown in FIG. 10.

Step 107: any seed unit is extracted from the parameter grids, the seed units are placed into the target subregion set, and the seed units and the units with the same attribute in the 8 adjacent units around the seed units are placed into the defined space set. And after the seed unit and the peripheral units with the same attribute are selected, deleting the seed unit from the definition space set. If there are grid cells in the definition space, one of the grids is defined as a seed cell. Repeating the above operations until the defined space is empty, stopping traversal, at this time, completely searching the sub-region where the first seed grid unit is located, selecting a new seed unit from the rest grid units, and repeating the above operations until all grid units have affiliated regions, where the process is shown in fig. 11.

Step 108: the process of sub-region boundary acquisition can be regarded as sorting edge nodes in a specified direction. A seed edge node is specified and any unconnected edge node can be selected as the seed node. The nearest unconnected one of the neighboring nodes will be connected one by one to the newly connected node.

According to the method, the curved surface can be automatically divided into a plurality of areas by inputting the target curved surface and the target machine tool parameters, so that the dynamic characteristics of the machine tool can be exerted to the maximum extent by tool paths planned in the same area by the same strategy, and the requirements of high-speed and high-precision machining are met. Aiming at the input curved surface to be processed, the method generates a group of grids according to the parameters such as the current parameter domain, compares the change state of each axis of the machine tool on the reference point of the grid unit, and marks labels on the grids according to the change state. And aggregating connected grids with the labels into a region through an aggregation algorithm, and finally acquiring a region boundary outline through a chain algorithm.