CN102490081A - Workpiece three-dimensional surface topography simulating method based on ball head milling - Google Patents
Workpiece three-dimensional surface topography simulating method based on ball head milling Download PDFInfo
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Abstract
The invention provides a workpiece three-dimensional surface topography modeling and simulating method based on the ball head milling. Firstly, a cutter location point influencing the generation of the three-dimensional surface topography in a simulation area is extracted, and a cutting edge sweeping point cloud model is established according to the combination of the extracted cutter location point with a kinematics model of a cutter in the processing process, then a three-dimensional surface topography sampling point within the range of the simulating area is set, and finally, the workpiece three-dimensional surface topography in the simulation area is formed. In the invention, the relation among the cutter parameters, the machining parameters and the workpiece three-dimensional surface topography is established, so that the three-dimensional surface topography under the condition of ultraprecision machining can be clearly represented, and the technological parameter optimization of the workpiece three-dimensional surface topography can be further realized.
Description
Technical Field
The invention relates to the field of ultra-precision machining, in particular to a modeling and simulation method for the three-dimensional surface appearance of a workpiece, which is particularly suitable for the workpiece machined by an ultra-precision ball-end milling cutter.
Background
With the development of national defense, aerospace, energy, medical treatment, optical component and other technologies and related industries, more and more basic equipment has put higher requirements on key parts such as aerospace gyros, computer magnetic drums, magnetic disks, multi-surface prisms, large-diameter aspherical mirrors, complex-shaped three-dimensional prisms and the like. The components have extremely high requirements on the processing precision, the surface roughness and the distribution of the three-dimensional surface appearance, and are processed by using conventional grinding, polishing and other methods, so that the processing cost is very high, the requirements on the precision and the surface roughness are difficult to meet at the same time, and a common machine tool is difficult to meet the high processing requirements, and the processing can be completed only by adopting an ultra-precision machine tool. At present, under the situation that the quality of the processed three-dimensional surface appearance becomes a focus of attention in the manufacturing industry, the requirements of various departments and research institutions on the three-dimensional surface appearance such as the surface shape precision, the waviness, namely the surface roughness of the ultra-precision processed part are higher and higher, and related researches are continuously carried out.
For almost half a century, researchers have continuously tried to meet the processing requirements by evaluating the three-dimensional surface topography of the workpiece to guide the formation process of the processing technique, and tried to find the relationship between the formation of the three-dimensional surface topography and the processing strategy and the processing parameters, thereby effectively controlling the formation process of the three-dimensional surface topography of the workpiece to a certain extent. The current study of three-dimensional surface topography is mainly carried out from two aspects: 1) measuring the three-dimensional surface appearance of the workpiece by an experiment; 2) and theoretically predicting the three-dimensional surface appearance of the workpiece. Although research on the three-dimensional surface topography formation mechanism and three-dimensional surface topography evaluation has achieved certain results from these two perspectives, defects and problems still exist, and the problems are mainly focused on measurement result analysis and three-dimensional surface topography algorithms. Because the measurement result of the three-dimensional surface topography of the workpiece is mainly the evaluation of the surface quality of the workpiece, the influence of the processing parameters and the processing strategy on the three-dimensional surface topography cannot be clearly represented, and the qualitative analysis is still mainly performed.
In the aspect of ultra-precise turning surface appearance modeling, much work is done at home and abroad. Such as: the super-precision ground surface topography modeling was studied by li-fir professor of hong kong theory of engineers, p.a. meyer, ca, chen dong xiang of tianjin university. But the research on the modeling of the ultra-precision milling surface appearance is less. In the aspect of simulating the surface morphology of the common ball head milling machining, many scholars also carry out research, such as the great Tan gang of northwest worker, the Zhangxianfeng of Shandong university, and the like. However, the target of the method is common milling, and the problems that the high precision in ultra-precision milling cannot be met or the calculation time is too long when the high precision is ensured and the like cannot be solved. The method describes a surface topography generation process from a material removal perspective, and performs cutting force analysis according to the process, but in the intersection point calculation process, a group of intersection points need to be calculated every time the spatial position of the blade is changed, and the calculation amount is large.
Disclosure of Invention
The invention aims to provide a workpiece three-dimensional surface morphology modeling and simulation method based on ultra-precision ball-end milling cutter machining. And expressing the three-dimensional surface morphology by using discrete point cloud data through the kinematic description of the cutting edge in the machining process. And dividing the simulation area according to the information of the processed curved surface and the number of the sampling points, establishing a follow-up containing box, and performing numerical analysis and spatial transformation on point cloud data in the containing box so as to obtain the processed three-dimensional surface morphology. The method overcomes the defect of low calculation precision in the traditional three-dimensional surface topography simulation method, is very suitable for high-precision ultra-precision machining, and can still keep good calculation efficiency under the requirement of high precision.
A modeling and simulation method for the three-dimensional surface topography of a workpiece comprises the following specific processes:
(one) selecting any region S on the processing surfacesim(u, v) as a simulation area, wherein u and v are parameter areas, and u belongs to [0, 1 ]]，v∈[0，1]。
Secondly, selecting a tool location point influencing the surface appearance of the simulation area in the existing machining tool path as a tool location point for three-dimensional surface appearance simulation according to the boundary information of the simulation area, and recording the line number of each line of tool paths and the initial tool location point of the tool path;
and (III) forming a three-dimensional surface appearance sweeping point cloud model according to the movement of the cutting edge by taking the tool location point selected in the step (II) as a movement node. The expression of the point cloud model of the blade swept point at any position in the blade position track is as follows:
wherein, B0Is a static edge discrete point coordinate matrix of a lower cutter in a cutter coordinate system (TCS), BiIs a discrete point coordinate matrix, T, of the cutting edge after the cutter moves under a workpiece coordinate system { WCS }1(T, N, theta) is a 4 x 4 transformation matrix rotating around the Z axis of the tool coordinate system, T2(t，p0，p1F) a 4X 4 transformation matrix for translation of the tool coordinate system relative to the workpiece coordinate system, tiIs from p0Point movement to p0、p1Any point p between pointsiThe elapsed time, N is the tool rotation speed, theta is the initial plunge phase angle, f is the tool feed speed, p0Simulating the starting tool location, p, for three-dimensional surface topography1A termination tool location point for three-dimensional surface topography simulation;
a point cloud B of discrete knife edges generated by all knife location points influencing the simulation areaiThe point cloud model of the blade sweep point of the simulation area is formed by overlapping.
And (IV) extracting three-dimensional surface topography control points:
setting the number p of sampling points of the three-dimensional surface topography of the simulation areau、pvWherein p isuNumber of samples in u direction, pvThe number of the samples in the v direction is further subjected to grid division on the simulation area, and grid nodes P are generatedknot(m, n) wherein m, n are integers and m.epsilon. [1, p ]u-1]，n∈[1，pv-1]；
The three-dimensional surface topography is characterized by PknotCharacterization point P at (m, n) nodes(m, n). Establishing a containing box on the simulation area grid, wherein the boundary direction of the containing box and the node Pknot(m, n) are parallel in normal loss direction at the position of a processed curved surface, the boundary of the containing box is the same as the corresponding grid boundary, the simulation area blade swept point cloud model in the step (three) is screened according to the containing box, and the point closest to the grid in the screening points is found out to be used as the three-dimensional surface topography characterization point P of the grid areas(m，n)。
Finally, traversing the grid of the simulation area according to the method to extract the control points of the three-dimensional surface topography on the simulation area, and finally obtaining the three-dimensional surface topography of the workpiece surface;
the invention establishes a workpiece three-dimensional surface appearance simulation model combining processing technological parameters, a cutter motion strategy and a cutter model on the basis of a three-dimensional surface appearance generation mechanism and a multi-axis numerical control processing theory, and the model fully considers the relationship among machine tool motion, cutter motion and three-dimensional surface appearance generation; and a three-dimensional surface appearance simulation algorithm independent of a machine tool structure is established on the basis, and the three-dimensional surface appearance characteristics of the workpiece under the machining condition of the ultra-precise ball-end milling cutter can be well represented.
According to the invention, a workpiece is processed according to a designed cutter path and process parameters, the surface of the workpiece is measured by the surface profile measuring instrument to obtain a three-dimensional surface appearance measured value, then the processed surface of the workpiece is simulated by the simulation method in the invention, and finally the simulated surface is compared with an experimental measured value, so that each characteristic of the three-dimensional surface appearance of the workpiece can be well represented. The method fully considers the influence of machine tool processing parameters and cutter motion strategies on the three-dimensional surface appearance, can carry out modeling and simulation on the three-dimensional surface appearance of the workpiece according to the existing cutter paths and processing parameters, and provides methods and means for optimizing the processing parameters and the cutter motion strategies for technologists.
Drawings
FIG. 1 is a schematic diagram of a tool location point extracted and participated in three-dimensional surface topography generation
FIG. 2 is a schematic view of the movement of a tool in a machine tool
FIG. 3 is a schematic diagram of the extraction of three-dimensional surface topography blade sweep points
FIG. 4 is a schematic diagram of three-dimensional surface topography feature point extraction
Detailed Description
The invention is further described with reference to the following figures and specific examples.
The method comprises the following specific implementation steps:
(1) setting a simulation area and extracting a tool location point influencing the three-dimensional surface appearance of the simulation area. To reduce the amount of computation, only the selected simulation region S needs to be affectedsimAnd (u, v) extracting the tool location points and modeling, so that unnecessary calculation can be reduced, and the characteristics of the three-dimensional surface appearance of the machined surface can be met.
As shown in FIG. 1, under the condition of three-axis machining, any region of the workpiece surface is selected as a simulation region S for no loss of generalitysim(u, v), and recording its boundaries:
E1，E2，E3and E4Respectively as simulation areas SsimFour boundary curves for (u, v).
Because the tool location point is on the tool location point offset surface, and the current boundary is selected on the processing curved surface, the boundary needs to be correspondingly offset calculated to be used as the condition for selecting the three-dimensional surface appearance modeling tool location point. The offset direction is the normal direction of the curve surface of each point on the boundary on the processing curve surface, the offset distance is the radius R of the cutter, so the method comprises the following steps:
E1off，E2off，E3offand E4offRespectively as simulation areas Ssim(u, v) four boundary curves after being biased.
And extracting tool location points according to a simulation area formed by the deviated boundary curve, finding out the tool location points in the area range as tool location points for three-dimensional surface topography modeling, storing the tool location points according to a feeding sequence, and simultaneously recording the starting points and the ending points of the tool paths in the simulation area for calculating subsequent cutting-in and cutting-out phase angles.
(2) And (3) establishing a point cloud model of the blade swept area according to the blade location points extracted in the step (1), as shown in fig. 2. The method comprises the following specific steps:
and (2.1) calculating a tool rotation matrix. Setting the coincidence of the cutter shaft and the Z axis of the cutter coordinate system, and then rotating torque matrix T under the cutter coordinate system1(tiN, θ) is as follows:
and (2.2) calculating a tool translation matrix. Tool position in machining processThe file coordinates are generated relative to the workpiece coordinate system, and in order to facilitate calculation, the tool coordinate system and the workpiece coordinate system are superposed under the initial modeling state, so that the moving process of the tool between any two tool positions can be calculated according to the generated tool position file. The moving process of the cutter between two cutter points in the three-axis machining is linear interpolation, namely t between the two cutter pointsiThe center coordinate of the cutter at the moment satisfies Pi＝P0+(P1-P0)/|(P1-P0)|×f×tiIn which P is0And P1Is the coordinate of two adjacent tool location points, tiIs from P0Beginning with PiThe elapsed time of the spot. To sum up, the tool translation matrix is:
wherein e1 T、e2 T、e3 TAre respectively a vector P0P1The X, Y, Z direction component of the unit vector.
And (2.3) calculating the space position of the blade between the two blade positions. The three-dimensional surface appearance of the workpiece is formed by cutting the workpiece by the cutting edge, the shape of the final workpiece surface depends on the envelope surface formed by the cutting edge in the cutting process, and the feeding speed, the rotating speed and the path of the cutter in the machining process determine that the motion of any point on the cutting edge is the spatial spiral motion. In order to represent the positions of the cutting edges at different moments in the machining process, delta omega is defined as a discrete parameter of the cutting edge position to segment simulation time, so that the generation of a point cloud of a cutting edge sweep point which is enough to meet simulation precision is ensured between two cutting edge positions.
Wherein t isiTo be driven fromP0 begins to PiThe elapsed time of a point, as a function of Δ ω versus time t (p)1-p0) Dispersing the tool bit f to obtain the position B of the discrete point of the tool edge at different dispersion moments between two tool positionsi。
Extracting simulated tool positions according to the step (1), sequentially executing the step (2) on two adjacent tool positions until obtaining tool edge swept point cloud models of all tool positions in a simulation area, and dispersing all tool edge points BiThe blade scanning point cloud model is formed by superposing the blade scanning point cloud model.
(3) And extracting three-dimensional surface appearance points according to the established blade swept point cloud model. Although the shape of the three-dimensional surface topography of the workpiece is determined by many factors, such as machine tool vibration, tool path, edge model, cutting parameters, and initial plunge phase angle, and many factors have uncertainties, such as machine tool vibration and tool distortion, these factors ultimately manifest themselves in the residual shape of the workpiece after the edge cuts the workpiece material, i.e., the final surface topography is determined by the final residual shape of the workpiece. Therefore, the extraction problem of the surface morphology is changed into the extraction of the envelope surface of the side, close to the processing curved surface, of the blade sweeping point, and the specific steps are as follows:
(3.1) obtaining a blade sweeping point of the simulation area according to the step (2)A cloud model, extracting a point cloud set B influencing the final surface appearanceextract。
As shown in FIG. 3, for the simulation region Ssim(u, v) forming an offset surface S by offsetting the cutting depth by the amount of cuttingsimoff(u, v) according to Ssim(u, v) and Ssimoff(u, v) extracting a point cloud of blade sweeps B between the two planesextract。
(3.2) for simulation region Ssim(u, v) sampling points p according to three-dimensional surface topographyu、pvDividing the grid, recording the node information P of each gridknot (m, n) and simulation region boundary information. Each grid area may correspond to a portion of the blade sweep point, as shown in FIG. 4, at PknotThe curved surface method at (m, n) is the boundary direction, the grid boundary is the boundary to establish a containing box, the point cloud in the containing box is used as the blade sweep point cloud B corresponding to the areabox(m，n)。
(3.3) extracting the corresponding blade sweep point cloud B in each grid containing boxboxThe point (m, n) nearest to the processing curved surface is taken as a characterization point P of the three-dimensional surface topography in the areas(m，n)。
As shown in fig. 4, in the blade point cloud in any grid container, a point is selected as a characteristic point of the region. In order to make the selected characterization point in the area representative of the area in the grid, the point closest to the processing surface is selected as the three-dimensional surface topography characterization point of the area.
With PknotMachining curved surface tangent, u-tangent, v-tangent and point P at (m, n) nodeknot(m, n) establishing an origin at Pknot(m, n) of a dynamic coordinate system { R (m, n) }. The set of radicals under { R (m, n) } can be represented as:
for finding the point closest to the curved surface to be machined, Pknot(m, n) grid corresponding blade sweep point cloud Bbox(m, n) to obtain BboxCoordinates in the coordinate system { R (m, n) } after (m, n) transformationR(m，n)Bbox(m，n)
Wherein,
t is a homogeneous transformation matrix from the workpiece coordinate system { WCS } to the dynamic coordinate system { R (m, n) }; extracting the { R (m, n) } coordinate systemR(m，n)BboxThe point with the minimum Z value in (m, n) is taken as the representation point of the three-dimensional surface topography in the area grid, and is inversely transformed to the workpiece coordinate system to obtain the corresponding topography feature point Ps(m, n). And (3.4) sequentially traversing all the grid points according to the step (3.3) until the three-dimensional surface topography characterization point in each grid area is positioned
All the coordinates under the workpiece coordinate system { WCS } are calculated, namely all the three-dimensional surface topography feature points P in the simulation areas。
Claims (5)
1. A modeling and simulation method for the three-dimensional surface topography of a workpiece comprises the following steps:
(one) selecting any region S on the processing surfacesim(u, v) is used as a simulation area, and a tool location point influencing the generation of the three-dimensional surface topography in the simulation area is selected from a tool location file according to the set boundary of the simulation area, wherein u and v are parameter areas, and u belongs to [0, 1 ]]，v∈[0，1]；
(II) establishing a blade swept point cloud model of a simulation area according to the extracted blade positions, wherein the blade swept point cloud model expression of any position in the blade position track is as follows:
wherein, B0The coordinate of the discrete point of the lower cutting edge is a cutting tool coordinate system { TCS }; b isiThe coordinate of the discrete point of the cutting edge in a workpiece coordinate system is obtained after the cutter is translated and rotated around the Z axis of the cutter; t is1(tiN, theta) is a 4 multiplied by 4 order rotation matrix rotating around the Z axis under the cutter coordinate system; t is2(ti，p0，p1，f0) Is a 4 x 4 order translation matrix of the tool coordinate system relative to the workpiece coordinate system; t is tiIs from p0Point movement to p0、p1Any point p between pointsiThe elapsed time; n is the rotational speed of the tool, theta is the phase angle of the cutting edge at the initial cutting, p0Simulating the starting tool location point coordinate, p, for three-dimensional surface topography1The coordinate of the cutter stopping point for simulating the three-dimensional surface appearance is shown, and f is the feeding speed of the cutter;
discrete point cloud B of blade edge generated on all blade points influencing simulation areaiThe point cloud model of the blade swept point in the simulation area is formed by overlapping the point cloud model and the blade swept point in the simulation area;
(III) extracting three-dimensional surface appearance control points to obtain the three-dimensional surface appearance of the workpiece
(1) Extracting a point cloud set B influencing the final surface appearance according to a point cloud model swept by the simulation region bladeextract；
(2) Setting the number p of sampling points of the three-dimensional surface topography of the simulation areau、pvWherein p isuNumber of samples in u direction, pvThe number of the samples in the v direction is further subjected to grid division on the simulation area, and grid nodes P are generatedknot(m, n) wherein m, n are integers and m.epsilon. [1, p ]u-1]，n∈[1，pv-1]；
(3) Establishing a containing box on the simulation area grid, wherein the containing box is bounded by the direction and the node Pknot(m, n) the normal vector directions are parallel at the processing curved surface, and the boundary of the containing box is the same as the boundary of the corresponding grid;
(4) through node PknotThe container box corresponding to (m, n) collects the point clouds BextractExtracting the point cloud in the containing box to form a point cloud Bbox(m, n) and finding out the point with the nearest distance to the grid as a characterization point P of the three-dimensional surface topography of the grid areas(m, n) are three-dimensional surface topography control points;
and generating the three-dimensional surface topography of the workpiece according to the three-dimensional surface topography control points.
2. The method for modeling and simulating the three-dimensional surface topography of a workpiece according to claim 1, wherein the establishment process of the point cloud model of the blade sweep point in the second step is as follows:
(1) determining a cutting edge phase angle at any position on a tool position track according to the tool position track, the machining parameters and the initial phase angle of each row of tool paths for machining the workpiece;
(2) and according to the machining parameters, the tool position points influencing the simulation area and the tool phase angles at any positions, obtaining a tool swept point cloud model by using a tool translation matrix and a rotation matrix.
3. The method for simulating the three-dimensional surface topography of the workpiece based on the ultra-precise three-axis milling process of the ball nose mill as claimed in claim 2, wherein the tool transformation matrix comprises a tool rotation matrix T1(tiN, theta) and tool translation matrix T2(ti，p0，p1And f) are respectively:
wherein e1 T、e2 T、e3 TAre respectively a vector P0P1The X, Y, Z direction component of the unit vector.
4. The method for simulating the three-dimensional surface topography of a workpiece based on the ultra-precise three-axis milling process of a ball nose mill as claimed in any one of claims 1 to 3, wherein in the third step, a point cloud set B influencing the final surface topography is extractedextractThe method specifically comprises the following steps: for simulation region Ssim(u, v) forming an offset surface Ssimoff(u, v) wherein the offset is the depth of cut, according to Ssim(u, v) and Ssimoff(u, v) extracting a point cloud set B of blade sweep points between the two curved surfacesextract。
5. The method for simulating the three-dimensional surface topography of the workpiece based on the ultra-precise three-axis milling process of the ball nose mill as claimed in one of claims 1 to 4, wherein in the third step, the point closest to the grid is found as the characterization point P of the three-dimensional surface topography of the grid regionsThe specific process of (m, n) is as follows:
first, with PknotMachining curved surface tangent, u-tangent, v-tangent and point P at (m, n) nodeknot(m, n) establishing a coordinate system { R (m, n) }, wherein a set of bases under the coordinate system { R (m, n) } can be expressed as:
wherein e is1(m，n)、e2(m，n)、e3(m, n) are three-way unit vectors of the coordinate system { R (m, n) },
secondly, screening out a point cloud set BextractIs included in the node Pknot(m, n) corresponding blade sweep points B in the housingbox(m, n) and for Bbox(m, n) transforming the coordinate system to obtain BboxCoordinates in the coordinate system { R (m, n) } after (m, n) transformationR(m，n)Bbox(m，n)：
Wherein
A transformation matrix for the coordinate system { R (m, n) } relative to the workpiece coordinate system { WCS };
then, search outR(m，n)BboxThe point with the minimum Z value in (m, n) is used as the point cloud set B of the blade sweep pointboxThe closest point in (m, n) to the grid, node Pknot(m, n) corresponding morphology control points;
finally, the point with the closest distance is inversely transformed into a workpiece coordinate system, and the final appearance characterization point P is obtaineds(m，n)。
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