CN111061218A - Complex curved surface machining cutting force prediction method and device based on ACIS - Google Patents
Complex curved surface machining cutting force prediction method and device based on ACIS Download PDFInfo
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Abstract
The invention belongs to the field of computer numerical control machining, and discloses a complex curved surface machining cutting force prediction method and device based on ACIS. The method comprises the following steps: adopting ACIS geometric modeling to construct a solid model of the envelope surface of the workpiece and the cutter; obtaining an engagement area and an engagement boundary between the workpiece and the tool enveloping body by using a Boolean intersection algorithm on the solid model; converting the meshing boundary under the global coordinate system into a meshing boundary under a cutter coordinate system; dispersing the meshing boundary of the cutter and the workpiece in the z-axis direction of a cutter coordinate system, and obtaining the radial immersion angle range of each infinitesimal position obtained by dispersion; the cutting force of each element is calculated according to the radial immersion angle, and then the elements in the meshing boundary are summed to obtain the cutting force of the whole cutter on the workpiece. The method can accurately obtain the meshing boundary and realize the prediction of the cutting force of the complex curved surface.
Description
Technical Field
The invention belongs to the field of computer numerical control machining, and particularly relates to a complex curved surface machining cutting force prediction method and device based on ACIS.
Background
Over the past century, companies and research institutes have made tremendous efforts to improve the performance of machining. By optimizing the tool geometry, cutting material, coolant and coating, tool life and machining performance are improved. However, there is no mature solution for predicting cutting force, especially for predicting cutting force of complex curved surface machining under a multi-axis machine tool.
Cutting forces directly affect the shape error and surface quality of the machined part. Once the cutting forces can be simulated, shape errors and vibrations caused by tool and workpiece deflections, as well as problems affecting surface quality, can be effectively predicted. The cutting force depends on the material of the tool and the workpiece, the geometry of the tool and the cutting conditions. In a great deal of previous research, the cutting force calculation of a smooth simple plane can be calculated by using an analytical method, a very mature theoretical result is formed, and commercial cutting force prediction software is introduced. However, for complex curved surfaces, due to the irregularity of the complex curved surfaces, it is difficult to obtain an accurate engagement boundary between the tool and the workpiece, so that the analytic method has not been well applicable in the calculation of the cutting force of the complex curved surfaces.
Disclosure of Invention
Aiming at the defects or improvement requirements of the prior art, the invention provides a complex curved surface machining cutting force prediction method and equipment based on ACIS, and aims to obtain a cutting boundary, a meshing area and a meshing boundary, perform discretization differential processing and calculate instantaneous cutting force by modeling the meshing condition of a tool and a workpiece in any contact state through three-dimensional model simulation by virtue of the modeling advantage of an ACIS engine, so as to realize the prediction of the complex curved surface cutting force.
To achieve the above object, according to an aspect of the present invention, there is provided an ACIS-based cutting force prediction method for complex curved surface machining, comprising the steps of:
(1) adopting ACIS geometric modeling to construct a solid model of the envelope surface of the workpiece and the cutter;
(2) on the established entity model of the workpiece and the tool enveloping surface, obtaining a meshing area between the workpiece and the tool enveloping body by using a Boolean intersection algorithm, and extracting the boundary of the meshing area so as to obtain the meshing boundary of the tool and the workpiece under a global coordinate system;
(3) converting the meshing boundary under the global coordinate system into a meshing boundary under a cutter coordinate system, wherein the cutter coordinate system takes a cutter location point as an original point, a cutter axis vector as a z-axis, and a rotating shaft of a cutter forward inclination angle and a rotating shaft of a cutter side inclination angle as an x-axis and a y-axis respectively;
(4) discretizing the meshing boundary of the cutter and the workpiece in the z-axis direction of the cutter coordinate system, and obtaining the radial immersion angle range of each infinitesimal position obtained by discretization;
(5) the cutting force of each element is calculated according to the radial immersion angle, and then the elements in the meshing boundary are summed to obtain the cutting force of the whole cutter on the workpiece.
Further, taking a world coordinate system XYZ as a global coordinate system, and modeling in the step (1) under the world coordinate system XYZ;
setting a process coordinate system FCN and a tool coordinate system xyz in the step (3), wherein:
the process coordinate system FCN takes the cutter location point as an origin, and an F axis, a C axis and an N axis are respectively parallel to an X axis, a Y axis and a Z axis of the world coordinate system;
the tool coordinate system xyz is obtained by rotating the process coordinate system FCN by the same angle around the axis C according to the size of the tool rake angle and then rotating by the same angle around the axis F according to the size of the tool side rake angle.
Further, the coordinate system is converted into an expression:
wherein T is a transformation matrix, l is a cutter rake angle, and T is a cutter roll angle.
Further, in step (4), the method for solving the radial immersion angle range is as follows:
setting a infinitesimal step length dz according to the meshing boundary outline under a tool coordinate system, decomposing a meshing region into a plurality of arc-shaped infinitesimals parallel to an xy plane along a z axis according to upper and lower boundaries zLow and zHigh of the meshing region in the z direction, and determining the z-axis coordinate z of the ith infinitesimaliThe expression of (a) is as follows:
zi＝zLOW+i×dz (3)
in the formula,
and i is an integer, zLow is the lower boundary of the meshing boundary, and zHigh is the upper boundary of the meshing boundary;
obtaining cut-in boundary and cut-out boundary on the meshing boundary contour through simulation, and obtaining coordinate z of ith infinitesimaliAfter, in ziMaking and cutting into the boundary at the location andcutting the intersection point of the boundary to obtain the corresponding radial immersion angle at the height
The upper and lower bounds of (1) are startAngle and endAngle, respectively.
Further, in the step (5),
in the case of each instantaneous cut, the cutting force is only generated if the cutting edge is in the region of engagement, so that for each cutting edge at each infinitesimal position ziRadial immersion angle of
If it is judged that
At [ startAngle, endAngle ]]In the range, the following calculation formula of infinitesimal force is used for solving the tangential, radial and axial forces of the cutting edge;
wherein, Ktc、Krc、Kac、Kte、Kre、KaeIs the coefficient of cut; the subscript j indicates the jth cutting edge on the tool; subscripts t, r, a are the t, r and a axes of a cutting edge coordinate system tra established in tangential, radial and axial directions of the cutting edge;
is the cutting thickness h of the jth cutting edgejWith respect to z-coordinate ziAnd radial immersion angle
A function of (a);
then, the following formula is used for conversion, and tangential, radial and axial forces of the cutting edge are converted into forces under a tool coordinate system;
wherein, TxyzThe matrix is a conversion matrix of a cutting edge coordinate system and a cutter coordinate system during forward milling or reverse milling;
and integrating the instantaneous tangential force, the instantaneous radial force and the instantaneous axial force on all the infinitesimal elements to obtain the cutting force of the whole cutter on the workpiece at the moment.
Further, TxyzIs a conversion matrix of a cutting edge coordinate system and a cutter coordinate system during forward milling:
wherein, KiFor the cutting edge at the infinitesimal position ziThe axial immersion angle is calculated as follows:
wherein,
is the position z in the engagement areaiRadius of the arc-shaped infinitesimal at (a).
To achieve the above object, the present invention also provides a computer-readable storage medium having stored thereon a computer program which, when executed by a processor, implements the method as described in any of the preceding claims.
In order to achieve the above object, the present invention further provides an ACIS-based cutting force prediction apparatus for complex curved surface machining, comprising the computer-readable storage medium as described above and a processor for calling and processing a computer program stored in the computer-readable storage medium.
In general, compared with the prior art, the above technical solution contemplated by the present invention can obtain the following beneficial effects:
(1) geometric and position information of the workpiece and the cutter enveloping surface is restored by ACIS modeling in a computer, an actual cutting process is simulated, the engagement boundary of the workpiece and the cutter at any moment can be obtained by solid Boolean operation, and the cutting force of the complex curved surface is calculated based on a discretization method, so that the problem that the engagement boundary is difficult to accurately obtain for the complex curved surface in the prior art is solved.
(2) Through the conversion of the world coordinate system and the tool coordinate system, the relation between the meshing area and the tool can be accurately obtained, so that the radial immersion angle of the tool can be determined.
(3) By dispersing the meshing area, the upper and lower bounds of the radial immersion angle at each infinitesimal position in the cutting process can be accurately obtained, and the judgment of the instantaneous cutting position is facilitated.
(4) Through the decomposition of the instantaneous cutting force under the cutting edge coordinate system and the conversion of the instantaneous cutting force under the cutter coordinate system, the cutting force components of each infinitesimal under the cutter coordinate system are obtained through solving, finally, the total cutting force of the whole meshing area can be obtained through integration, and the prediction of the cutting force of the cutter at any moment is realized.
Drawings
FIG. 1 is a flow chart of the cutting force prediction method for ACIS-based complex curved surface machining according to the present invention;
FIG. 2 is a block diagram of a solid model of a workpiece and tool created using ACIS;
FIG. 3 is a diagram of the area of engagement of the workpiece and the tool using a Boolean algorithm;
FIG. 4 is a schematic representation of the rake and roll angles;
FIG. 5 is a schematic diagram of a coordinate system and engagement boundaries;
FIG. 6 is a schematic view of the engagement boundary abutting the tool surface;
FIG. 7 is a schematic diagram of a meshing boundary cut-in and cut-out position in a tool coordinate system;
FIG. 8 is a schematic view of a discrete method of cutting force modeling.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
As shown in fig. 1, the method for predicting the cutting force of the present invention comprises the steps of:
1. constructing a solid model of the envelope surface of the workpiece and the cutter in a computer by utilizing an ACIS geometric modeling engine;
3D
modeler (acis) is a three-dimensional geometric modeling engine with higher precision, supports a robust 3D modeling function, and is an ideal tool for constructing an application program with a hybrid modeling function. The work of modeling the envelope surfaces of the workpiece and tool can be performed using the SDK of the ACIS C + + version, the modeling portion of the example being shown in FIG. 2.
2. On the established entity model, obtaining a meshing area between the workpiece and the tool enveloping body by using a Boolean intersection algorithm, and extracting the boundary to obtain the meshing boundary of the tool workpiece under the global coordinate system;
in ACIS, all models are represented using the three-dimensional B-Rep method. The basic idea of the B-Rep method is to define an entity as a finite space enclosed by closed boundary surfaces, which can be represented by a subset of faces, which are defined by edges, edges by points, points and finally by three coordinate values. In the underlying data structure, the topological graph is used for representation, so the boolean intersection algorithm of the B-Rep method is to calculate the common part between the topological graphs of the two entity model underlayers, and the boolean operation result of the example is shown in fig. 3. And the boundary of the engagement region of the sheet is the engagement boundary.
3. Mapping the meshing boundary under the global coordinate system to the tool coordinate system
In total, three coordinate systems are established throughout the process, which are described below as the world coordinate system, the process coordinate system and the tool coordinate system.
The world coordinate system XYZ is a fixed coordinate system, and the whole modeling process is completed under the world coordinate system in step 1.
The process coordinate system FCN is an intermediate coordinate system established for the sake of conversion, wherein the origin of the process coordinate system is at the center of the sphere of the ball nose tool, and the three axes FCN are respectively parallel to the XYZ axes of the world coordinate system.
The tool coordinate system xyz origin is also at the tool position, and is obtained by rotating the process coordinate system around the C axis by the anteversion angle and then rotating the process coordinate system around the F axis by the laterial inclination angle.
A schematic of the process and tool coordinate systems is shown in fig. 4, and a schematic of the rake and roll angles is shown in fig. 5.
During the process of moving the ball end mill relative to a workpiece coordinate system (namely a world coordinate system), the ball end mill predicts the original point of the action point of milling force in a process coordinate system FCN, so that the action point of the predicted force makes relative translation motion in the world coordinate system. Meanwhile, because the force is a vector, the magnitude and the direction of the force only need to be considered, only the coordinate transformation from the process coordinate system to the tool coordinate system needs to be calculated, and because the original points are consistent, only two rotations need to be carried out. The coordinate system is transformed into the expression:
wherein T is a transformation matrix, l is a cutter rake angle, and T is a cutter roll angle.
Three coordinate systems are established in ACIS by the above method and the position of the engagement boundary in space is shown, as shown in fig. 6. The coordinates of the meshing boundary in space are converted into coordinates in the tool coordinate system using the above conversion formula, and thus can be attached to the tool surface, as shown in fig. 7.
4. The coordinate positions of the cutting-in position and the cutting-out position in the tool coordinate system can be obtained through the above process, as shown in fig. 8. Because of the general discrete cutting force model, the cutting force on each infinitesimal element is calculated firstly, and the cutting forces on all the infinitesimal elements are superposed, thereby obtaining the cutting force on the whole cutter. In this example, the selected discretization method discretizes the z-direction in the tool coordinate system as shown in FIG. 8. First, the upper and lower limits of the meshing boundary in the z-direction, such as zLow and zHigh in fig. 8, need to be obtained, and then the infinitesimal step length dz is set, so that the z-axis coordinate z of the ith infinitesimal isiThe expression of (a) is as follows:
zi＝zLOW+i×dz (3)
in the formula,
i is an integer, zLow is the lower boundary of the meshing boundary, and zHigh is the upper boundary of the meshing boundary;
obtaining cut-in boundary and cut-out boundary on the meshing boundary contour through simulation, and obtaining coordinate z of ith infinitesimaliAfter, in ziMaking a plane parallel to the xy plane at the position to obtain the intersection point of the xy plane and the cut-in boundary and the cut-out boundary so as to obtain the radial immersion angle corresponding to the height
The upper and lower bounds of (1) are startAngle and endAngle, respectively.
(5) Cutting at each instantIn the case of (2), the cutting force is generated only when the cutting edge is in the engagement region,
wherein, Ktc、Krc、Kac、Kte、Kre、KaeThe cutting coefficient can be obtained through a calibration test according to different cutter workpiece materials; the subscript j indicates the jth cutting edge on the tool; subscripts t, r, a are the t, r and a axes of a cutting edge coordinate system tra established in tangential, radial and axial directions of the cutting edge;
is the cutting thickness h of the jth cutting edgejWith respect to z-coordinate ziAnd radial immersion angle
A function of (a);
then, the following formula is used for conversion, and tangential, radial and axial forces of the cutting edge are converted into forces under a tool coordinate system;
wherein, TxyzThe matrix is a conversion matrix of a cutting edge coordinate system and a cutter coordinate system during forward milling or reverse milling;
and integrating the instantaneous tangential force, the instantaneous radial force and the instantaneous axial force on all the infinitesimal elements to obtain the cutting force of the whole cutter on the workpiece at the moment.
Taking the straight milling as an example, the conversion matrix of the cutting edge coordinate system and the tool coordinate system during the straight milling is as follows:
wherein, KiFor the cutting edge at the infinitesimal position ziThe axial immersion angle is calculated as follows:
wherein,
is the position z in the engagement areaiRadius of the arc-shaped infinitesimal at (a).
The forward milling and the reverse milling have corresponding adjustment in the form of a conversion matrix due to different tool turning directions, but the overall calculation method is the same as that of the forward milling and is not repeated.
After the forces on all the infinitesimal elements are obtained, the forces on all the infinitesimal elements are integrated, and then the cutting force of the whole cutter on the workpiece at the moment can be obtained.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (8)
1. The method for predicting the cutting force of the complex curved surface machining based on the ACIS is characterized by comprising the following steps of:
(1) adopting ACIS geometric modeling to construct a solid model of the envelope surface of the workpiece and the cutter;
(2) on the established entity model of the workpiece and the tool enveloping surface, obtaining a meshing area between the workpiece and the tool enveloping body by using a Boolean intersection algorithm, and extracting the boundary of the meshing area so as to obtain the meshing boundary of the tool and the workpiece under a global coordinate system;
(3) converting the meshing boundary under the global coordinate system into a meshing boundary under a cutter coordinate system, wherein the cutter coordinate system takes a cutter location point as an original point, a cutter axis vector as a z-axis, and a rotating shaft of a cutter forward inclination angle and a rotating shaft of a cutter side inclination angle as an x-axis and a y-axis respectively;
(4) discretizing the meshing boundary of the cutter and the workpiece in the z-axis direction of the cutter coordinate system, and obtaining the radial immersion angle range of each infinitesimal position obtained by discretization;
(5) the cutting force of each element is calculated according to the radial immersion angle, and then the elements in the meshing boundary are summed to obtain the cutting force of the whole cutter on the workpiece.
2. An ACIS-based cutting force prediction method for complex curved surface machining based on the claim 1, characterized in that, the world coordinate system XYZ is taken as the global coordinate system, and modeling is performed in the step (1) under the world coordinate system XYZ;
setting a process coordinate system FCN and a tool coordinate system xyz in the step (3), wherein:
the process coordinate system FCN takes the cutter location point as an origin, and an F axis, a C axis and an N axis are respectively parallel to an X axis, a Y axis and a Z axis of the world coordinate system;
the tool coordinate system xyz is obtained by rotating the process coordinate system FCN by the same angle around the axis C according to the size of the tool rake angle and then rotating by the same angle around the axis F according to the size of the tool side rake angle.
3. An ACIS-based cutting force prediction method for complex curved surface machining according to claim 2, wherein the coordinate system is transformed into the expression:
wherein T is a transformation matrix, l is a cutter rake angle, and T is a cutter roll angle.
4. An ACIS-based cutting force prediction method for complex curved surface machining according to claim 2 or 3, wherein in step (4), the method for solving the radial immersion angle range is as follows:
setting a infinitesimal step length dz according to the meshing boundary outline under a tool coordinate system, decomposing a meshing region into a plurality of arc-shaped infinitesimals parallel to an xy plane along a z axis according to upper and lower boundaries zLow and zHigh of the meshing region in the z direction, and determining the z-axis coordinate z of the ith infinitesimaliThe expression of (a) is as follows:
zi＝zLOW+i×dz (3)
in the formula,
and i is an integer, zLow is the lower boundary of the meshing boundary, and zHigh is the upper boundary of the meshing boundary;
obtaining cut-in boundary and cut-out boundary on the meshing boundary contour through simulation, and obtaining coordinate z of ith infinitesimaliAfter, in ziMaking the intersection point of the cut-in boundary and the cut-out boundary at the position to obtain the corresponding radial immersion angle at the height
The upper and lower bounds of (1) are startAngle and endAngle, respectively.
5. An ACIS-based cutting force prediction method for complex curved surface machining according to claim 4, wherein in step (5),
in the case of each instantaneous cut, the cutting force is only generated if the cutting edge is in the region of engagement, so that for each cutting edge at each infinitesimal position ziRadial immersion angle of
If it is judged that
At [ startAngle, endAngle ]]In the range, the following calculation formula of infinitesimal force is used for solving the tangential, radial and axial forces of the cutting edge;
wherein, Ktc、Krc、Kac、Kte、Kre、KaeIs the coefficient of cut; the subscript j indicates the jth cutting edge on the tool; subscripts t, r, a are the t, r and a axes of a cutting edge coordinate system tra established in tangential, radial and axial directions of the cutting edge;
is the cutting thickness h of the jth cutting edgejWith respect to z-coordinate ziAnd radial immersion angle
A function of (a);
then, the following formula is used for conversion, and tangential, radial and axial forces of the cutting edge are converted into forces under a tool coordinate system;
wherein, TxyzThe matrix is a conversion matrix of a cutting edge coordinate system and a cutter coordinate system during forward milling or reverse milling;
and integrating the instantaneous tangential force, the instantaneous radial force and the instantaneous axial force on all the infinitesimal elements to obtain the cutting force of the whole cutter on the workpiece at the moment.
6. The ACIS-based cutting force prediction method for complex curved surface machining according to claim 5, wherein T isxyzIs a conversion matrix of a cutting edge coordinate system and a cutter coordinate system during forward milling:
wherein, KiFor the cutting edge at the infinitesimal position ziThe axial immersion angle is calculated as follows:
wherein,
is the position z in the engagement areaiRadius of the arc-shaped infinitesimal at (a).
7. A computer-readable storage medium, having stored thereon a computer program which, when executed by a processor, implements the method of any one of claims 1 to 6.
8. An ACIS-based complex machining cutting force prediction apparatus comprising the computer-readable storage medium of claim 7 and a processor for invoking and processing the computer program stored in the computer-readable storage medium.
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