CN102490081A

CN102490081A - Workpiece three-dimensional surface topography simulating method based on ball head milling

Info

Publication number: CN102490081A
Application number: CN2011103595763A
Authority: CN
Inventors: 彭芳瑜; 方正隆; 吴警; 闫蓉; 李斌
Original assignee: Huazhong University of Science and Technology
Current assignee: Huazhong University of Science and Technology
Priority date: 2011-11-14
Filing date: 2011-11-14
Publication date: 2012-06-13
Anticipated expiration: 2031-11-14
Also published as: CN102490081B

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

Simulation Method of 3D Surface Topography of Workpiece Based on Ball Nose Milling

技术领域 technical field

本发明涉及超精密加工领域，具体为一种工件三维表面形貌的建模及仿真方法，尤其适用于采用超精密球头铣刀加工的工件。The invention relates to the field of ultra-precision machining, in particular to a method for modeling and simulating three-dimensional surface topography of workpieces, and is especially suitable for workpieces processed by ultra-precision ball end milling cutters.

背景技术 Background technique

随着国防、航空航天、能源、医疗、光学元器件等技术和相关行业的发展，越来越多的基础装备对一些关键零部件如宇航陀螺，计算机磁鼓、磁盘，多面棱镜，大直径非球面镜，以及复杂形状的立体棱镜等提出了更高的要求。这类元器件对加工精度、表面粗糙度和三维表面形貌分布要求极高，使用常规的磨削、研磨、抛光等方法进行加工，不但加工成本很高，而且难以同时满足精度和表面粗糙度的要求，普通机床更是难以满足如此高的加工要求，必须采用超精密机床才能够完成加工。目前在加工三维表面形貌的质量成为制造业关注热点的形势下，各个部门及研究机构对超精密加工零件的表面形状精度、波纹度、即表面粗糙度等三维表面形貌的要求越来越高，相关研究也在不断进行。With the development of national defense, aerospace, energy, medical, optical components and other technologies and related industries, more and more basic equipment is required for some key components such as aerospace gyroscopes, computer drums, disks, polygonal prisms, large-diameter Spherical mirrors, and stereoscopic prisms with complex shapes put forward higher requirements. Such components have extremely high requirements on processing accuracy, surface roughness and three-dimensional surface topography distribution. Using conventional grinding, grinding, polishing and other methods for processing, not only the processing cost is high, but also it is difficult to meet the accuracy and surface roughness at the same time. It is even more difficult for ordinary machine tools to meet such high processing requirements, and ultra-precision machine tools must be used to complete the processing. At present, under the situation that the quality of processed three-dimensional surface topography has become a hot spot in the manufacturing industry, various departments and research institutions have more and more requirements for three-dimensional surface topography such as surface shape accuracy, waviness, and surface roughness of ultra-precision machined parts. High, related research is also ongoing.

近半个多世纪以来，研究人员不断的尝试通过评定工件的三维表面形貌来指导加工工艺的形成过程来满足加工要求，试图找到三维表面形貌形成与加工策略及加工参数的关系，从而有效的对工件三维表面形貌的形成过程在一定程度上进行控制。目前对三维表面形貌的研究主要从两个方面进行：1)实验测量工件三维表面形貌；2)理论预测工件三维表面形貌。虽然从这两个角度出发对三维表面形貌形成机理以及三维表面形貌评定的研究已经取得了一定成果，但是缺陷和问题仍然存在，问题主要集中在测量结果分析和三维表面形貌算法上。由于工件三维表面形貌的测量结果主要是对工件表面质量的评定，所以不能清楚表征加工参数以及加工策略对三维表面形貌的影响，仍主要出于定性分析。For more than half a century, researchers have been trying to guide the formation process of the machining process by evaluating the three-dimensional surface topography of the workpiece to meet the processing requirements, trying to find the relationship between the formation of the three-dimensional surface topography and the processing strategy and processing parameters, so as to effectively The formation process of the three-dimensional surface topography of the workpiece is controlled to a certain extent. At present, the research on the three-dimensional surface topography is mainly carried out from two aspects: 1) experimentally measuring the three-dimensional surface topography of the workpiece; 2) theoretically predicting the three-dimensional surface topography of the workpiece. Although some achievements have been made in the research on the formation mechanism of 3D surface topography and the evaluation of 3D surface topography from these two perspectives, defects and problems still exist. The problems mainly focus on the analysis of measurement results and the algorithm of 3D surface topography. Since the measurement results of the three-dimensional surface topography of the workpiece are mainly for the evaluation of the surface quality of the workpiece, the inability to clearly characterize the influence of processing parameters and processing strategies on the three-dimensional surface topography is still mainly due to qualitative analysis.

在超精密车削表面形貌建模方面，国内外做了较多工作。如：香港理工大学的李荣彬教授，加拿大的P.A.Meyer等，天津大学的陈东祥对超精密磨削的表面形貌建模进行了研究。但在超精密铣削加工表面形貌建模方面，研究较少。在球头铣削普通加工表面形貌仿真方面，很多学者也进行了研究，如西北工大的谭刚，山东大学的张孝峰等。但其针对的对象均是普通铣削加工，不能满足超精密铣削加工中的高精度或者在保证高精度时计算时间过长等问题。该方法从材料去除角度描述表面形貌生成过程，并且根据该过程进行切削力分析，但在计算交点过程中刀刃每变换一次空间位置就需要计算一组交点，计算量较大。In the aspect of ultra-precision turning surface topography modeling, a lot of work has been done at home and abroad. Such as: Professor Li Rongbin of Hong Kong Polytechnic University, P.A.Meyer of Canada, etc., and Chen Dongxiang of Tianjin University have studied the surface topography modeling of ultra-precision grinding. However, there are few studies on surface topography modeling in ultra-precision milling. Many scholars have also conducted research on the simulation of surface topography in general machining of ball-end milling, such as Tan Gang from Northwestern University of Technology, Zhang Xiaofeng from Shandong University, etc. However, it is aimed at ordinary milling, which cannot meet the high precision of ultra-precision milling or the calculation time is too long when high precision is guaranteed. This method describes the surface topography generation process from the perspective of material removal, and analyzes the cutting force according to the process. However, in the process of calculating the intersection point, a set of intersection points needs to be calculated every time the cutting edge changes its spatial position, which requires a large amount of calculation.

发明内容 Contents of the invention

本发明的目的在于提供一种基于超精密球头铣刀加工的工件三维表面形貌建模及仿真方法。通过对刀刃在加工过程中的运动学描述，将三维表面形貌用离散点云数据表达。根据加工曲面信息和采样点数目对仿真区域进行划分并建立随动包容盒，对包容盒内点云数据进行数值分析和空间变换，从而获取加工三维表面形貌。本方法解决了以往三维表面形貌仿真方法中计算精度低的缺点，非常适合于高精度的超精密加工，而且在高精度的要求下，仍能保持不错的计算效率。The object of the present invention is to provide a method for modeling and simulating three-dimensional surface topography of workpieces based on ultra-precision ball end milling cutter processing. Through the kinematic description of the cutting edge during the machining process, the three-dimensional surface topography is expressed by discrete point cloud data. According to the processing surface information and the number of sampling points, the simulation area is divided and a dynamic containment box is established, and the point cloud data in the containment box is numerically analyzed and spatially transformed to obtain the processed 3D surface topography. This method solves the shortcomings of low calculation accuracy in the previous three-dimensional surface topography simulation methods, and is very suitable for high-precision ultra-precision machining, and can still maintain good calculation efficiency under the high-precision requirements.

一种工件三维表面形貌的建模及仿真方法，具体过程如下：A method for modeling and simulating a three-dimensional surface topography of a workpiece, the specific process is as follows:

(一)在加工表面上选取任意区域S_sim(u，v)作为仿真区域，其中，u、v为参数域，u∈[0，1]，v∈[0，1]。(1) Select any area S _sim (u, v) on the machined surface as the simulation area, where u, v are parameter domains, u∈[0,1], v∈[0,1].

(二)根据仿真区域边界信息，选取已有加工刀具路径中影响仿真区域表面形貌的刀位点作为三维表面形貌仿真的刀位点，并记录每行刀路的行数以及刀路的起始刀位点；(2) According to the boundary information of the simulation area, select the tool position points that affect the surface topography of the simulation area in the existing machining tool path as the tool position points for the three-dimensional surface topography simulation, and record the number of lines of each line of tool paths and the number of tool paths starting tool position;

(三)以步骤(二)所选取的刀位点作为运动节点，根据刀刃运动形成三维表面形貌扫掠点云模型。刀位轨迹中任意位置的刀刃扫掠点云模型表达式为：(3) Using the knife position selected in step (2) as the motion node, a three-dimensional surface topography sweep point cloud model is formed according to the blade motion. The expression of the blade sweep point cloud model at any position in the tool trajectory is:

其中，B₀为刀具坐标系{TCS}下刀具静态刃部离散点坐标矩阵，B_i为工件坐标系{WCS}下刀具运动后的刀刃离散点坐标矩阵，T₁(t，N，θ)为刀具坐标系下绕自身Z轴旋转的4×4变换矩阵，T₂(t，p₀，p₁，f)为刀具坐标系相对于工件坐标系平移的4×4变换矩阵，t_i为从p₀点运动到p₀、p₁点之间任意点p_i所经历时间，N为刀具转速，θ为初始切入相位角，f为刀具进给速度，p₀为三维表面形貌仿真起始刀位点，p₁为三维表面形貌仿真的终止刀位点；Among them, B ₀ is the coordinate matrix of the discrete points of the static edge of the tool in the tool coordinate system {TCS}, B _i is the coordinate matrix of the discrete points of the blade after the tool moves in the workpiece coordinate system {WCS}, T ₁ (t, N, θ) is the 4×4 transformation matrix that rotates around its own Z axis in the tool coordinate system, T ₂ (t, p ₀ , p ₁ , f) is the 4×4 transformation matrix that translates the tool coordinate system relative to the workpiece coordinate system, and t _i is The time elapsed from point p ₀ to any point p _i between points p ₀ and p ₁ , N is the tool rotation speed, θ is the initial cut-in phase angle, f is the tool feed rate, p ₀ is the start of three-dimensional surface topography simulation The starting knife position, p ₁ is the ending knife position of the three-dimensional surface topography simulation;

将影响仿真区域所有刀位点产生的刀刃离散点云B_i叠加在一起就构成了仿真区域刀刃扫掠点云模型。The point cloud model of the blade sweep in the simulation area is formed by superimposing the blade discrete point cloud B _i generated by all the knife position points in the simulation area.

(四)三维表面形貌控制点提取：(4) Extraction of three-dimensional surface topography control points:

设定仿真区域三维表面形貌采样点数p_u、p_v，其中p_u为u向采样数目，p_v为v向采样数目，进而对仿真区域进行网格划分，生成网格节点P_knot(m，n)，其中m、n为整数且m∈[1，p_u-1]，n∈[1，p_v-1]；Set the number of sampling points p _u and p _v of the three-dimensional surface topography in the simulation area, where p _u is the number of samples in the u direction, and p _v is the number of samples in the v direction, and then mesh the simulation area to generate grid nodes P _knot (m , n), where m, n are integers and m∈[1, p _u -1], n∈[1, p _v -1];

三维表面形貌的表征是由P_knot(m，n)节点处的表征点P_s(m，n)来控制。在仿真区域网格上建立包容盒，包容盒边界方向与节点P_knot(m，n)在加工曲面处法失方向平行，包容盒边界与对应网格边界相同，根据此包容盒对步骤(三)中仿真区域刀刃扫掠点云模型进行筛选，并找出筛选点中离网格距离最近点作为该网格区域三维表面形貌表征点P_s(m，n)。The characterization of the three-dimensional surface topography is controlled by the characteristic point P _s (m, n) at the node of P _knot (m, n). Establish a containment box on the grid of the simulation area, the boundary direction of the containment box is parallel to the normal direction of the node P _knot (m, n) at the processing surface, and the boundary of the containment box is the same as the corresponding grid boundary. According to the containment box, the steps (three ) to filter the point cloud model of the knife edge sweep in the simulation area, and find out the point closest to the grid among the screened points as the 3D surface topography characterization point P _s (m, n) of the grid area.

最后根据上述方法遍历仿真区域网格实现仿真区域上三维表面形貌控制点的提取，并最终得到工件表面的三维表面形貌；Finally, according to the above method, the grid of the simulation area is traversed to realize the extraction of the three-dimensional surface topography control points on the simulation area, and finally the three-dimensional surface topography of the workpiece surface is obtained;

本发明以三维表面形貌生成机理及多轴数控加工理论为基础，建立了一种结合加工工艺参数、刀具运动策略以及刀具模型的工件三维表面形貌仿真模型，该模型充分考虑到了机床运动、刀具运动以及三维表面形貌生成的关系；并在此基础之上建立了一种独立于机床结构的三维表面形貌仿真算法，能够很好的表征超精密球头铣刀加工条件下工件三维表面形貌特征。Based on the three-dimensional surface topography generation mechanism and multi-axis numerical control machining theory, the present invention establishes a workpiece three-dimensional surface topography simulation model that combines processing parameters, tool movement strategies and tool models. The model fully takes into account machine tool movement, The relationship between tool movement and 3D surface topography generation; and on this basis, a 3D surface topography simulation algorithm independent of the machine tool structure is established, which can well characterize the three-dimensional surface of the workpiece under the processing conditions of ultra-precision ball end milling cutters Morphological features.

本发明根据已设计好的刀具路径及工艺参数加工出的工件，通过表面轮廓测量仪对其表面进行测量获得三维表面形貌测量值，然后利用本发明中的仿真方法对其加工表面进行仿真，并最终与实验测量值进行对比，能够很好的表征工件三维表面形貌的各个特征。本发明充分考虑了机床加工参数以及刀具运动策略对三维表面形貌的影响，可以根据已有的刀具路径和加工参数对工件三维表面形貌进行建模及仿真，为工艺人员提供优化加工参数和刀具运动策略的方法和手段。In the present invention, according to the workpiece processed by the designed tool path and process parameters, the surface is measured by the surface profile measuring instrument to obtain the three-dimensional surface topography measurement value, and then the simulation method in the present invention is used to simulate the processed surface. And finally compared with the experimental measurement value, it can well characterize the various characteristics of the three-dimensional surface topography of the workpiece. The present invention fully considers the influence of machine tool processing parameters and tool motion strategies on the three-dimensional surface topography, and can model and simulate the three-dimensional surface topography of the workpiece according to the existing tool paths and processing parameters, and provide technicians with optimized processing parameters and Methods and means for tool motion strategies.

附图说明 Description of drawings

图1为提取参与三维表面形貌生成刀位点示意图Figure 1 is a schematic diagram of the extraction of knife positions involved in the generation of 3D surface topography

图2为刀具在机床运动过程示意图Figure 2 is a schematic diagram of the tool movement process in the machine tool

图3为提取三维表面形貌刀刃扫掠点示意图Figure 3 is a schematic diagram of the blade sweep points for extracting 3D surface topography

图4为三维表面形貌特征点提取示意图Figure 4 is a schematic diagram of the extraction of three-dimensional surface topography feature points

具体实施方式 Detailed ways

下面结合附图和具体实施例对本发明作进一步说明。The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

本发明具体实施步骤如下：The specific implementation steps of the present invention are as follows:

(1)设定仿真区域并提取影响仿真区域三维表面形貌的刀位点。为了减少计算量，只需要将影响选定仿真区域S_sim(u，v)的刀位点提取出来进行建模即可，这样既可以减少无谓的计算也可以满足加工表面三维表面形貌的特征。(1) Set the simulation area and extract the tool points that affect the three-dimensional surface topography of the simulation area. In order to reduce the amount of calculation, it is only necessary to extract the tool position points that affect the selected simulation area S _sim (u, v) for modeling, which can reduce unnecessary calculations and meet the characteristics of the three-dimensional surface topography of the machined surface .

如图1所示，在三轴加工条件下，为不失一般性，选取工件表面的任意区域作为仿真区域S_sim(u，v)，并记录其边界：As shown in Fig. 1, under the condition of three-axis machining, without loss of generality, any area on the workpiece surface is selected as the simulation area S _sim (u, v), and its boundary is recorded:

$\{\begin{matrix} {E E.}_{11} = = {S S}_{sim sim} ((u u,, v v)) {| |}_{u u = = 00} \\ {E E.}_{22} = = {S S}_{sim sim} ((u u,, v v)) {| |}_{u u = = 11} \\ {E E.}_{33} = = {S S}_{sim sim} ((u u,, v v)) {| |}_{v v = = 00} \\ {E E.}_{44} = = {S S}_{sim sim} ((u u,, v v)) {| |}_{v v = = 11} \end{matrix}$

E₁，E₂，E₃和E₄分别为仿真区域S_sim(u，v)的四条边界曲线。E ₁ , E ₂ , E ₃ and E ₄ are four boundary curves of the simulation area S _sim (u, v) respectively.

由于刀位点在刀位点偏置面上，而目前的边界是在加工曲面上选取的，所以需要对该边界进行相应偏置计算才可以作为选题三维表面形貌建模刀位点的条件。偏置方向为边界上各点在加工曲面上该点的曲面法失方向，偏置距离为刀具半径R，故有：Since the tool point is on the offset surface of the tool point, and the current boundary is selected on the processing surface, it is necessary to perform corresponding offset calculations on the boundary before it can be used as the tool point of the selected topic for 3D surface topography modeling. condition. The offset direction is the surface normal direction of each point on the processing surface at the point on the boundary, and the offset distance is the tool radius R, so:

$\{\begin{matrix} {E E.}_{11 off off} = = {E E.}_{11} + + R R \times \times &PartialD; &PartialD; {S S}_{sim sim} ((u u,, v v)) / / &PartialD; &PartialD; u u \times \times &PartialD; &PartialD; {S S}_{sim sim} ((u u,, v v)) / / &PartialD; &PartialD; v v {| |}_{u u = = 00} \\ {E E.}_{22 off off} = = {E E.}_{22} + + R R \times \times &PartialD; &PartialD; {S S}_{sim sim} ((u u,, v v)) / / &PartialD; &PartialD; u u \times \times {&PartialD; &PartialD; S S}_{sim sim} ((u u,, v v)) / / &PartialD; &PartialD; v v {| |}_{u u = = 11} \\ {E E.}_{33 off off} = = {E E.}_{33} + + R R \times \times &PartialD; &PartialD; {S S}_{sim sim} ((u u,, v v)) / / &PartialD; &PartialD; u u \times \times &PartialD; &PartialD; {S S}_{sim sim} ((u u,, v v)) / / &PartialD; &PartialD; v v {| |}_{v v = = 00} \\ {E E.}_{44 off off} = = {E E.}_{44} + + R R \times \times &PartialD; &PartialD; {S S}_{sim sim} ((u u,, v v)) / / &PartialD; &PartialD; u u \times \times &PartialD; &PartialD; {S S}_{sim sim} ((u u,, v v)) / / &PartialD; &PartialD; v v {| |}_{v v = = 11} \end{matrix}$

E_1off，E_2off，E_3off和E_4off分别为仿真区域S_sim(u，v)的四条边界曲线经偏置后的边界曲线。E _1off , E _2off , E _3off and E _4off are respectively the offset boundary curves of the four boundary curves of the simulation region S _sim (u, v).

根据偏置后的边界曲线所形成的仿真区域进行刀位点提取，找出在区域范围内的刀位点作为三维表面形貌建模的刀位点，并且按照走刀顺序进行保存，同时记录各条刀具路径在仿真区域内的起始点和终止点，用作后续切入以及切出相位角的计算。According to the simulation area formed by the offset boundary curve, the tool position points are extracted, and the tool position points within the area are found as the tool position points for 3D surface topography modeling, and are saved according to the order of the cutting tool, and recorded at the same time The start and end points of each tool path in the simulation area are used for the calculation of the subsequent cut-in and cut-out phase angles.

(2)根据(1)中提取出的刀位点，建立刀刃扫掠点云模型，如图2所示。具体步骤如下：(2) According to the knife position points extracted in (1), establish the point cloud model of the blade sweep, as shown in Figure 2. Specific steps are as follows:

(2.1)刀具旋转矩阵计算。设定刀轴与刀具坐标系Z轴重合，则刀具坐标系下旋转矩阵T₁(t_i，N，θ)的计算公式如下：(2.1) Calculation of tool rotation matrix. Assuming that the tool axis coincides with the Z axis of the tool coordinate system, the calculation formula of the rotation matrix T ₁ (t _i , N, θ) in the tool coordinate system is as follows:

${T T}_{11} (({t t}_{i i},, N N,, θ θ)) = = [\begin{matrix} cos cos ((θ θ + + N N \times \times 22 π π / / 6060 \times \times {t t}_{i i})) & sin sin ((θ θ + + N N \times \times 22 π π / / 6060 \times \times {t t}_{i i})) & 00 & 00 \\ - - sin sin ((θ θ + + N N \times \times 22 π π / / 6060 \times \times {t t}_{i i})) & cos cos ((θ θ + + N N \times \times 22 π π / / 6060 \times \times {t t}_{i i})) & 00 & 00 \\ 00 & 00 & 11 & 00 \\ 00 & 00 & 00 & 11 \end{matrix}]$

(2.2)刀具平移矩阵计算。加工过程中的刀位文件坐标是相对于工件坐标系生成的，为了使计算方便，在建模初始状态下将刀具坐标系与工件坐标系重合，则刀具在任一两刀位点之间的移动过程可根据已生成的刀位文件计算得到。三轴加工中刀具在两刀位点之间的移动过程为直线插补，即两刀位点之间t_i时刻刀具中心坐标满足P_i＝P₀+(P₁-P₀)/|(P₁-P₀)|×f×t_i，其中P₀和P₁为相邻两刀位点坐标，t_i为从P₀开始到P_i点所经历时间。综上所述，刀具平移矩阵为：(2.2) Calculation of tool translation matrix. The tool position file coordinates in the machining process are generated relative to the workpiece coordinate system. In order to facilitate the calculation, the tool coordinate system and the workpiece coordinate system are coincident in the initial modeling state, and the tool moves between any two tool positions The process can be calculated according to the generated tool location file. In three-axis machining, the moving process of the tool between two tool positions is linear interpolation, that is, the coordinates of the tool center at time t _i between the two tool positions satisfy P _i =P ₀ +(P ₁ -P ₀ )/|( P ₁ -P ₀ )|×f×t _i , where P ₀ and P ₁ are the coordinates of two adjacent knife points, and t _i is the time elapsed from P ₀ to P _i . In summary, the tool translation matrix is:

${T T}_{22} (({t t}_{i i},, {p p}_{00},, {p p}_{11},, f f)) = = [\begin{matrix} 11 & 00 & 00 & 00 \\ 00 & 11 & 00 & 00 \\ 00 & 00 & 11 & 00 \\ {P P}_{00} + + f f \times \times {t t}_{i i} \times \times (({P P}_{11} - - {P P}_{00})) / / | | (({P P}_{11} - - {P P}_{00})) | | \times \times {e e}_{11}^{T T} & {P P}_{00} + + f f \times \times {t t}_{i i} \times \times (({P P}_{11} - - {P P}_{00})) / / | | (({P P}_{11} - - {P P}_{00})) | | \times \times {e e}_{22}^{T T} & {P P}_{00} + + f f \times \times {t t}_{i i} \times \times (({P P}_{11} - - {P P}_{00})) / / | | (({P P}_{11} - - {P P}_{00})) | | \times \times {e e}_{33}^{T T} & 11 \end{matrix}]$

其中e₁ ^T、e₂ ^T、e₃ ^T分别为矢量P₀P₁的单位矢量的X、Y、Z方向的分量。Where e ₁ ^T , e ₂ ^T , and e ₃ ^T are components in the X, Y, and Z directions of the unit vector of the vector P ₀ P _1, respectively.

(2.3)计算两刀位点之间刀刃空间位置。工件三维表面形貌是刀刃切削工件形成的，最终工件表面的形状取决于刀刃在切削过程中形成的包络面，而刀具在加工过程中进给速度、刀具转速和刀具路径决定了刀刃上任意一点的运动为空间螺旋运动。为了表示刀刃在加工过程中不同时刻的位置，定义Δω作为刀刃位置的离散参数对仿真时间进行分割，以保证在两刀位点之间有足够满足仿真精度的刀刃扫掠点点云生成。(2.3) Calculate the spatial position of the blade between the two knife positions. The three-dimensional surface morphology of the workpiece is formed by the cutting edge of the workpiece. The final shape of the workpiece surface depends on the envelope surface formed by the cutting edge during the cutting process, and the feed rate, tool speed and tool path of the tool determine any shape on the cutting edge. The movement of one point is space spiral movement. In order to represent the position of the blade at different moments in the machining process, Δω is defined as the discrete parameter of the blade position to divide the simulation time, so as to ensure that there are enough blade sweep point cloud generation between the two blade positions to meet the simulation accuracy.

其中t_i为从_P0开始到P_i点所经历时间，根据Δω对时间t＝(p₁-p₀)/f进行离散，得到计算两刀位点之间不同离散时刻下的刀刃离散点位置B_i。Among them, t _i is the time elapsed from _P 0 to P _i point, according to Δω, the time t=(p ₁ -p ₀ )/f is discretized, and the discretized point of the blade at different discretized moments between the two knife positions can be obtained position B _i .

根据步骤(1)中提取出到仿真刀位点，对其中相邻两刀位点依次执行步骤(2)直到得到仿真区域所有刀位点的刀刃扫掠点云模型，将这些所有的刀刃离散点B_i叠加在一起就构成了刀刃扫掠点云模型。According to the simulated knife position extracted in step (1), step (2) is performed in turn for two adjacent knife positions until the blade sweep point cloud model of all knife positions in the simulation area is obtained, and all these knife edges are discretized The point B _i is superimposed to form the blade sweep point cloud model.

(3)根据建立的刀刃扫掠点云模型提取三维表面形貌点。虽然工件三维表面形貌的形状有许多因素决定，例如机床振动、刀具路径、刀刃模型、切削参数和初始切入相位角等，并且许多影响因素具有不确定性，例如机床振动和刀具变形，但这些因素最终都会表现在刀刃切削工件材料后的残留形状，即最终的表面形貌由工件最终的残留形状决定。因而，表面形貌的提取问题变成了刀刃扫掠点靠近加工曲面一侧的包络面提取，具体步骤如下：(3) Extract the three-dimensional surface topography points according to the established blade sweep point cloud model. Although the shape of the three-dimensional surface topography of the workpiece is determined by many factors, such as machine vibration, tool path, cutting edge model, cutting parameters and initial cut-in phase angle, etc., and many influencing factors have uncertainties, such as machine vibration and tool deformation, but these Factors will eventually be reflected in the residual shape of the workpiece after the cutting edge cuts the material, that is, the final surface morphology is determined by the final residual shape of the workpiece. Therefore, the problem of surface topography extraction becomes the envelope surface extraction of the edge sweep point close to the processing surface. The specific steps are as follows:

(3.1)根据步骤(2)得到了仿真区域刀刃扫掠点云模型，提取出影响最终表面形貌的点云集合B_extract。(3.1) According to the step (2), the blade-swept point cloud model of the simulation area is obtained, and the point cloud set B _extract that affects the final surface morphology is extracted.

如图3所示，对仿真区域S_sim(u，v)进行偏置，偏置量为切削深度，形成偏置面S_simoff(u，v)，根据S_sim(u，v)和S_simoff(u，v)提取出位于这两个平面之间的刀刃扫掠点云B_extract。As shown in Figure 3, the simulation area S _sim (u, v) is offset, and the offset amount is the cutting depth to form an offset surface S _simoff (u, v), according to S _sim (u, v) and S _simoff (u, v) extracts the blade-swept point cloud B _extract located between these two planes.

(3.2)对仿真区域S_sim(u，v)按照三维表面形貌采样点数p_u、p_v划分网格，记录每个网格节点信息P_knot(m，n)和仿真区域边界信息。每一个网格区域可以对应一部分刀刃扫掠点，如图4所示，以P_knot(m，n)处曲面法失为边界方向、网格边界为边界建立包容盒，位于包容盒内的点云作为该区域对应的刀刃扫掠点云B_box(m，n)。(3.2) The simulation area S _sim (u, v) is divided into grids according to the three-dimensional surface topography sampling points p _u and p _v , and the information of each grid node P _kno t(m, n) and the boundary information of the simulation area are recorded. Each grid area can correspond to a part of the blade sweep points, as shown in Figure 4, the surface method at P _knot (m, n) is used as the boundary direction, and the grid boundary is used as the boundary to establish a containment box, and the points located in the containment box The cloud is used as the blade-swept point cloud B _box (m, n) corresponding to this area.

(3.3)提取每个网格包容盒内对应刀刃扫掠点云B_box(m，n)中离加工曲面最近的点，作为该区域内三维表面形貌的表征点P_s(m，n)。(3.3) Extract the nearest point to the processing surface in the corresponding blade sweep point cloud B _box (m, n) in each grid containment box, as the representative point P _s (m, n) of the three-dimensional surface topography in the area .

如图4所示，在任意一个网格包容盒内的刀刃点云中，选取一个点作为该区域的表征点。为了使该区域内选取的表征点对该网格内区域具有代表性，需要选取其中到加工曲面距离最近的点作为该区域的三维表面形貌表征点。As shown in Figure 4, in any point cloud of the blade in the enclosing box of a grid, a point is selected as the representative point of the area. In order to make the selected characterization points in this area representative of the area in the grid, it is necessary to select the point with the closest distance to the processed surface as the 3D surface topography characterization point of this area.

以P_knot(m，n)结点处加工曲面法失、u向切失、v向切失和点P_knot(m，n)建立原点在P_knot(m，n)的动态坐标系{R(m，n)}。{R(m，n)}下的一组基可表示为： _The dynamic coordinate system _{ _R (m,n)}. A set of basis under {R(m,n)} can be expressed as:

$\{\begin{matrix} {e e}_{11} ((m m,, n no)) = = \frac{&PartialD; &PartialD; {S S}_{sim sim} ((u u,, v v)) / / &PartialD; &PartialD; u u}{| | &PartialD; &PartialD; {S S}_{sim sim} ((u u,, v v)) / / &PartialD; &PartialD; u u | |} {| |}_{u u = = m m,, v v = = n no} \\ {e e}_{22} ((m m,, n no)) = = \frac{&PartialD; &PartialD; {S S}_{sim sim} ((u u,, v v)) / / &PartialD; &PartialD; v v}{| | &PartialD; &PartialD; {S S}_{sim sim} ((u u,, v v)) / / &PartialD; &PartialD; v v | |} {| |}_{u u = = m m,, v v = = n no} \\ {e e}_{33} ((m m,, n no)) = = \frac{&PartialD; &PartialD; {S S}_{sim sim} ((u u,, v v)) / / &PartialD; &PartialD; u u \times \times &PartialD; &PartialD; {S S}_{sim sim} ((u u,, v v)) / / &PartialD; &PartialD; v v}{| | &PartialD; &PartialD; {S S}_{sim sim} ((u u,, v v)) / / &PartialD; &PartialD; u u \times \times &PartialD; &PartialD; {S S}_{sim sim} ((u u,, v v)) / / &PartialD; &PartialD; v v | |} {| |}_{u u = = m m,, v v = = n no} \end{matrix}$

为找到离加工曲面距离最近的点，对P_knot(m，n)网格对应刀刃扫掠点云B_box(m，n)进行位姿变换，获得B_box(m，n)变换后在坐标系{R(m，n)}下的坐标^R(m，n)B_box(m，n)In order to find the point closest to the processing surface, the P _knot (m, n) grid corresponds to the blade sweep point cloud B _box (m, n) for pose transformation, and after the B _box (m, n) transformation is obtained, the coordinates Coordinates R(m, n) B _box ( ^{m, n) under the system {R(m} , n)}

$[\begin{matrix} {{B B}_{box box} ((m m,, n no))}_{R R ((m m,, n no))} \\ 11 \end{matrix}] {= =}_{w w}^{R R ((m m,, n no))} T T \times \times [\begin{matrix} {B B}_{box box} ((m m,, n no)) \\ 11 \end{matrix}]$

其中，

T为从工件坐标系{WCS}到动态坐标系{R(m，n)}的齐次变换矩阵；提取{R(m，n)}坐标系下^R(m，n)B_box(m，n)中Z值最小的点作为该区域网格中的三维表面形貌的表征点，并进行逆变换到工件坐标系下，得到对应形貌特征点P_s(m，n)。(3.4)按照(3.3)步骤依次遍历所有网格点直到每个网格区域中的三维表面形貌表征点在in,

T is the homogeneous transformation matrix from the workpiece coordinate system {WCS} to the dynamic coordinate system {R(m, n)}; extract ^{R(m, n)} B _box (m, The point with the smallest Z value in n) is used as the representative point of the three-dimensional surface topography in the grid of the area, and is inversely transformed into the workpiece coordinate system to obtain the corresponding topography feature point P _s (m, n). (3.4) According to the step (3.3), traverse all the grid points in turn until the three-dimensional surface topography characterization points in each grid area are at

工件坐标系{WCS}下坐标全部算出，即仿真区域中全部三维表面形貌特征点P_s。All coordinates in the workpiece coordinate system {WCS} are calculated, that is, all three-dimensional surface topography feature points P _s in the simulation area.

Claims

1. A modeling and simulation method of a three-dimensional surface topography of a workpiece, comprising the steps of:

(1) Select any area S _sim (u, v) on the processing surface as the simulation area, and select the tool position points in the tool position file that affect the generation of the three-dimensional surface topography in the simulation area according to the set simulation area boundary, Among them, u and v are parameter fields, u∈[0,1], v∈[0,1];

(2) According to the extracted knife position points, establish the blade sweep point cloud model in the simulation area, and the knife edge sweep point cloud model expression at any position in the knife position trajectory is:

Among them, B ₀ is the coordinate of the discrete point of the blade in the tool coordinate system {TCS}; B _i is the coordinate of the discrete point of the blade in the workpiece coordinate system after the tool is translated and rotated around its own Z-axis; T ₁ (t _i , N, θ) is the 4×4 order rotation matrix around the Z axis in the tool coordinate system; T ₂ (t _i , p ₀ , p ₁ , f ₀ ) is the 4×4 order translation matrix of the tool coordinate system relative to the workpiece coordinate system ; t _i is the time elapsed from point p ₀ to any point p _i between p ₀ and p ₁ ; N is the tool speed, θ is the phase angle of the cutting edge at the initial cutting, p ₀ is the start of three-dimensional surface topography simulation Coordinates of the starting tool position, p ₁ is the coordinates of the ending tool position of the three-dimensional surface topography simulation, and f is the tool feed rate;

The knife edge discrete point cloud B _i generated for all knife position points in the simulation area is superimposed together to form the blade sweep point cloud model of the simulation area;

(3) Extract the control points of the three-dimensional surface topography to obtain the three-dimensional surface topography of the workpiece

(1) According to the blade-swept point cloud model in the simulation area, extract the point cloud set B _extract that affects the final surface topography;

(2) Set the number of sampling points p _u and p _v of the three-dimensional surface topography in the simulation area, where p _u is the number of samples in the u direction, and p _v is the number of samples in the v direction, and then divide the simulation area into grids to generate grid nodes P _knot (m, n), where m, n are integers and m ∈ [1, p _u -1], n ∈ [1, p _v -1];

(3) Establish a containment box on the grid of the simulation area, the boundary direction of the containment box is parallel to the normal vector direction of the node P _knot (m, n) at the processing surface, and the boundary of the containment box is the same as the corresponding grid boundary;

(4) Through the containment box corresponding to the node P _knot (m, n), extract the point cloud in the containment box in the point cloud set B _extract to form a point cloud B _box (m, n), and find out the The point closest to the grid distance is used as the characteristic point P _s (m, n) of the three-dimensional surface topography of the grid area, which is the three-dimensional surface topography control point;

According to the above three-dimensional surface topography control points, the three-dimensional surface topography of the workpiece can be generated.

2. the modeling and simulation method of a kind of workpiece three-dimensional surface topography according to claim 1, it is characterized in that, in the above-mentioned steps (two), the establishment process of blade sweeping point cloud model is as follows:

(1) According to the tool position trajectory of workpiece processing, processing parameters and the initial phase angle of each row of tool paths, the phase angle of the blade at any position on the tool position trajectory is determined;

(2) According to the machining parameters, the tool positions affecting the simulation area and the phase angle of the blade at any position, the blade sweep point cloud model can be obtained by using the tool translation matrix and rotation matrix.

3. according to a kind of workpiece three-dimensional surface topography simulation method based on ball end mill ultra-precision three-axis milling process described in claim 2, it is characterized in that, described tool transformation matrix comprises tool rotation matrix T ₁ (t _i , N, θ) and tool translation matrix T ₂ (t _i , p ₀ , p ₁ , f) are:

Where e ₁ ^T , e ₂ ^T , and e ₃ ^T are components in the X, Y, and Z directions of the unit vector of the vector P ₀ P _1, respectively.

4. A method for simulating the three-dimensional surface topography of a workpiece based on ultra-precision three-axis milling with a ball-end milling cutter according to any one of claims 1-3, characterized in that, in the above-mentioned step (3), the final The point cloud set B _extract of the surface topography is specifically: offset the simulation area S _sim (u, v) to form an offset surface S _simoff (u, v), where the offset is the cutting depth, according to S _sim ( u, v) and S _simoff (u, v) to extract the blade sweep point cloud set B _extract located between these two surfaces.

5. A kind of workpiece three-dimensional surface topography simulation method based on ball end milling cutter ultra-precision three-axis milling according to one of claims 1-4, characterized in that, in the step (3), find out where The specific process of using the point closest to the grid as the representative point P _s (m, n) of the three-dimensional surface topography of the grid area is:

Firstly, the coordinate system {R(m, n)} is established with the point P _knot (m, n) to process the normal loss, u-direction cut-off, v-direction cut-off and point P _knot (m, n) of the surface, where the coordinate A set of basis under the system {R(m,n)} can be expressed as:

Among them, e ₁ (m, n), e ₂ (m, n), e ₃ (m, n) are the three-way unit vectors of the coordinate system {R(m, n)} respectively,

Secondly, filter out the blade sweep point B box (m, n) contained in the containing box corresponding to the node P _knot (m, n) in the point cloud set B _extract , and coordinate _{the B box} ₍ m, n) Transform to obtain the coordinate R(m, n) B _box (m, n) in the coordinate system {R ⁽ m, n)} after B _box (m, n) transformation:

in

is the transformation matrix of the coordinate system {R(m, n)} relative to the workpiece coordinate system {WCS};

Then, search for the point with the smallest Z value in ^{R(m, n)} B _box (m, n) as the point closest to the grid distance in the blade sweep point cloud set B _box (m, n), that is The shape control point corresponding to the node P _knot (m, n);

Finally, the point with the closest distance is inversely transformed into the workpiece coordinate system, that is, the final shape characteristic point P _s (m, n) is obtained.