WO2020125040A1 - 基于矢量场的曲面分区加工轨迹拓扑形状设计方法 - Google Patents

基于矢量场的曲面分区加工轨迹拓扑形状设计方法 Download PDF

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WO2020125040A1
WO2020125040A1 PCT/CN2019/101266 CN2019101266W WO2020125040A1 WO 2020125040 A1 WO2020125040 A1 WO 2020125040A1 CN 2019101266 W CN2019101266 W CN 2019101266W WO 2020125040 A1 WO2020125040 A1 WO 2020125040A1
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vector
vector field
cutting
height error
point
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French (fr)
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马建伟
贾振元
鲁晓
姜文文
赵孝轩
刘巍
司立坤
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大连理工大学
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Priority to US16/753,206 priority Critical patent/US11429081B2/en
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00—Programme-control systems
    • G05B19/02—Programme-control systems electric
    • G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
    • G05B19/19—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by positioning or contouring control systems, e.g. to control position from one programmed point to another or to control movement along a programmed continuous path
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00—Programme-control systems
    • G05B19/02—Programme-control systems electric
    • G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
    • G05B19/402—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by control arrangements for positioning, e.g. centring a tool relative to a hole in the workpiece, additional detection means to correct position
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00—Programme-control systems
    • G05B19/02—Programme-control systems electric
    • G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
    • G05B19/416—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by control of velocity, acceleration or deceleration
    • G05B19/4166—Controlling feed or in-feed
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
    • B23C—MILLING
    • B23C3/00—Milling particular work; Special milling operations; Machines therefor
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00—Program-control systems
    • G05B2219/30—Nc systems
    • G05B2219/35—Nc in input of data, input till input file format
    • G05B2219/35167—Automatic toolpath generation and tool selection
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00—Program-control systems
    • G05B2219/30—Nc systems
    • G05B2219/37—Measurements
    • G05B2219/37355—Cutting, milling, machining force

Definitions

  • the invention belongs to the technical field of high-precision and high-efficiency milling of complex curved surface parts, and relates to a method for designing a topological shape of a curved surface partition machining trajectory based on a vector field.
  • the patent of Hao Xiaozhong et al. "Divisional mapping method of NC machining tool path considering the regional distribution of errors", publication number CN107145126A.
  • the patent generates a theoretical tool path based on the theoretical surface of the workpiece, compares the actual surface of the workpiece with the theoretical surface to obtain the error distribution rule, divides the actual surface according to the error distribution rule, and selects the corresponding tool path mapping method for the area of different error types.
  • Theoretical tool path mapping to the actual surface of the workpiece completes the tool path mapping process.
  • the partitioning results of this method are susceptible to measurement errors, and the method of comparing the actual and theoretical surfaces in the partitioning process lacks theoretical support, so this partitioning method has greater limitations.
  • This method divides the processing area into concave area, convex area and saddle area by calculating the Gaussian curvature and average curvature of each point on the curved surface, and plans different processing techniques for different areas to achieve a significant increase in processing efficiency.
  • this method does not take into account the smoothness of the feed motion during the machining process.
  • the topological shape design of the machining trajectory lacks a theoretical basis and has certain limitations.
  • the present invention proposes a topological shape design method of curved surface partition machining trajectory based on vector field.
  • the division of the machining area and the trajectory planning lack comprehensive consideration of the tooling method and feed motion stability, resulting in local error outliers and significant cutting vibration.
  • the constrained tool vector field realizes the initial division of the machining area based on the tool vector distribution and the subdivision of the machining area to ensure a stable feed motion.
  • the topological shape design of the complex curved parts is completed. This effectively improves the machining accuracy of the surface division processing and the stability of the feed movement, providing technical support for the high-precision and efficient machining of complex curved surfaces.
  • the technical solution of the present invention is a topological shape design method for surface zoning machining trajectories based on a vector field, which is characterized in that the method respectively establishes a functional relationship between chord height/residual height error and the normal curvature of the cutting direction, that is, chord height error and residual height
  • the coordinate vector field of the error co-constraint is normalized to construct a two-objective two-objective optimization model.
  • the optimal vector direction is solved by constructing the evaluation function to establish the space vector field; the plane vector field divergence after projection is calculated and Curl, classify the vector field according to whether it is zero, realize the initial division of the processing area; analyze the characteristics of different vector fields, fit the streamline of the space vector field, the kinematic parameters of the feed motion of the rotation axis of the computer bed along the streamline, according to its Whether to complete the subdivision of the processing area by mutation; combine the tooling method to realize the topological shape design of the processing trajectory of different processing areas of the curved surface; the specific steps of the method are as follows:
  • Step 1 Establish a coordinated vector field of chord height error and residual height error
  • k f is the normal curvature of the cutting direction.
  • the residual height error h is calculated as:
  • k d is the normal curvature in the line spacing direction and r is the effective radius of the tool.
  • H is the average curvature, for any point on the surface, H is a fixed value.
  • chord height error and residual height error are only determined by the normal curvature of the cutting direction.
  • a two-objective optimization model is constructed with two types of errors as the objective functions.
  • k 1 and k 2 represent the main curvature of the surface (k 1 > k 2 ), which is calculated as:
  • K is Gaussian curvature, for any point on the surface, K is a fixed value.
  • chord height error The maximum value of chord height error is:
  • the minimum chord height error is:
  • the string height error and residual height error that appear later are normalized string height error and residual height error.
  • the dual objective optimization model is established as:
  • V-min represents the minimization of the vector, that is, the two sub-objective functions e n and h n in the vector target are as small as possible;
  • ⁇ 1 and ⁇ 2 are the weights of chord height error and residual height error in the evaluation function, and their calculations are as follows:
  • h n1 is the residual height error corresponding to the minimum chord height error
  • en n1 is the corresponding chord height error when the residual height error is minimum
  • h nmin is the minimum residual height error
  • e nmin is the minimum chord height error.
  • the optimal solution of the bi-objective optimization model is calculated as follows:
  • ⁇ is the angle between the cutting direction and k 1 corresponding to the main direction, at this time,
  • E, F, and G are the first-class basic quantities of curved surfaces
  • L, M, and N are the second-class basic quantities of curved surfaces, which are expressed as follows:
  • a, b, c are expressed as:
  • the optimal cutting direction of each point on the surface is obtained by solving, and a unit cutting vector is established along this direction, thereby forming a coordinated cutting vector field of chord height error and residual height error.
  • Step 2 Initial division of the machining area based on the distribution of the pass vector
  • the knife vector distribution is regional. For the vector field with regional tool vector distribution, the initial division of the machining area based on the tool vector distribution is carried out.
  • the distribution of the pass vectors in the vector field can be determined.
  • the divergence divA( ⁇ * ) at any point in the plane vector field A( ⁇ * ) (f 1 (x, y), f 2 (x, y)) is calculated as:
  • k is the unit vector along the positive direction of the z-axis of the rectangular coordinate system in space.
  • the corresponding vector field types in different processing areas are determined, and the sudden change points of divergence or curl in the plane vector field are mapped onto the surface, and the fitting curve is used as the boundary of different processing areas.
  • Step 3 ensure the subdivision of the machining area with stable feed motion
  • step 2 Combining the results of the initial division of the processing area in step 2, streamline fitting the space vector fields of different processing areas, and developing the processing area to ensure the stable feed motion according to the kinematic parameters of the feed motion of the machine axis along the vector field flow line Subdivision.
  • the rotary axis of the rotary table A is parallel to the X axis of the machine coordinate system
  • the rotary axis of the rotary table C is parallel to the Z axis of the machine coordinate system.
  • the streamline of the space vector field in the processing area is r( ⁇ ), where ⁇ is the arc length parameter of the streamline equation.
  • Su (u ( ⁇ ), v ( ⁇ )), S v (u ( ⁇ ), v ( ⁇ )) are the first-order partial derivatives of the curved surface S (u, v) at the streamline.
  • angles ⁇ A ( ⁇ ) and ⁇ C ( ⁇ ) of the machine tool A and C axes are:
  • t represents the processing time
  • v represents the set feed rate
  • ⁇ represents the set stationary coefficient
  • ⁇ the smoother the feed motion
  • its value range is generally 1-5
  • s the total arc length of the streamline.
  • Step 4 Topological shape design of machining trajectories in different machining areas of curved surfaces
  • the complex curved surface is divided into different processing areas with regular distribution of the cutting tool vectors and stable feed motion along the flow field of the vector field. Combined with the cutting tool method, a suitable topological shape design of the processing path is carried out for each processing area.
  • the distribution of the pass vectors of each point of this type of flat vector field is parallel, so the line cut pass is used for processing.
  • Streamline fitting is performed by using the cutting vector of each point as the tangent to the machining trajectory to generate a parallel two-dimensional machining trajectory.
  • the distribution of the cutting tool vectors at each point of this type of flat vector field presents a vortex state.
  • the streamline is a complete vortex line, which is processed by a circular cutting tool; when the area boundary curve and vector
  • the streamlines are local vortex lines, which are processed by line cutting.
  • Streamline fitting is performed by using the cutting vectors of each point as the tangent to the machining trajectory to generate a spiral two-dimensional machining trajectory.
  • the distribution of the cutting tool vectors at various points in this type of flat vector field is in a radiated state, so line cutting cutting tools are used.
  • Streamline fitting is performed by using the cutting vector of each point as the tangent to the machining trajectory to generate a radial two-dimensional machining trajectory.
  • the distribution of the cutting tool vectors at various points in this type of flat vector field is irregular, and it is not suitable to use line cutting or circular cutting tool processing, so the scattered and rotating fields are converted into non-scattering and non-rotating fields.
  • the vector distribution presents a parallel state, so the vector adjustment for the scattered and rotating field passes is as follows:
  • Streamline fitting is performed by using the adjusted cutting tool vector at each point as the trajectory of the machining trajectory to generate a parallel two-dimensional machining trajectory.
  • the two-dimensional machining trajectory is mapped onto the curved surface to obtain the three-dimensional machining trajectory, thereby realizing the topological shape design of the curved surface partition machining trajectory based on the vector field.
  • the significant effect and benefit of the present invention is to propose a topological shape design method for surface zoning machining trajectories based on vector fields.
  • This method is aimed at the complex surface zoning process, and the machining area segmentation and trajectory planning lack the tooling mode and feed motion. Stability comprehensively considers the local error outliers and significant cutting vibration caused by the problem.
  • Stability comprehensively considers the local error outliers and significant cutting vibration caused by the problem.
  • the machining area is subdivided, and the topological shape design of the zoning machining trajectory of complex curved surface parts is finally realized, which effectively reduces the processing error of the zoning processing of the curved surface, improves the smoothness of the feed motion, and provides technical support for the high-precision and efficient processing of complex curved surfaces.
  • Figure 1 Overall flow chart of the method
  • Figure 2 Step vector field of chord height error and residual height error coordinated constraint
  • Figure 3 Preliminary division of the machining area based on the cutter vector distribution and subdivision of the machining area to ensure stable feed motion
  • Figure 4 The topological shape of the processing trajectory designed by a single processing area
  • Figure 5 a) represents the roughness of the processed surface using the traditional overall processing method
  • b) represents the processing using the partitioned processing method of the present invention Surface roughness
  • Ra represents the roughness of the processed surface ( ⁇ m)
  • Figure 6 Comparison of the contours of the processed surface measured by the three-dimensional coordinate measuring machine using the traditional integral processing method and the partitioned processing method of the present invention.
  • the embodiment adopts an AC double-turntable five-axis numerical control machine tool, taking a complex curved surface with high steepness, frequency unevenness, and sudden change of curvature as an example, and using UG software and MATLAB software to explain in detail the implementation process of the present invention.
  • the complex surface is modeled using UG software, with a symmetrical slewing surface with a local steepness of 60° as the main body, two irregular pits are designed on the slewing surface, and then a high steepness, frequency irregularity, and curvature are established
  • the complex surface with catastrophic features is shown in Figure 3.
  • equations (1)-(5) establish the functional relationship between the chord height/residual height error of each point on the surface and the normal curvature of the cutting direction/line spacing direction, and normalize the two types of errors through equations (6)-(12) Processing, using MATLAB software, through equations (13)-(24) to construct and solve a two-objective optimization model of two types of errors to obtain the optimal cutting direction of each point, and then establish a coordinated cutting vector of chord height error and residual height error ⁇ See Figure 2.
  • the plane vector field is obtained by projecting the space vector field.
  • the divergence and curl of each point of the plane vector field are calculated by equations (25)-(26), where the maximum and minimum values of the divergence are 0.2299, respectively. And 0, the maximum and minimum curl values are 0.1191 and 0.0045, respectively.
  • the plane vector field is classified, and the curve fitted by the divergence or curl change point is used as the partition boundary to complete the initial division of the processing area of the complex surface.
  • the concave part of the curved surface corresponds to the scattered whirl field, and the rest corresponds to the non-scattered whirl field.
  • the topological shapes of the machining trajectories in different machining areas are designed.
  • the complex curved pits have scattered and rotating fields. Adjust the point vectors according to equation (33). See Figure 4 for the corresponding line-cutting machining trajectories. The rest are non-scattering and rotating fields. Considering the regional boundaries and vector field streamlines, the corresponding line-cutting and ring-cutting trajectories are generated to complete the surface segmentation based on the vector field. Topological shape design of machining track.
  • the surface roughness of the curved surface obtained by the traditional overall processing is 3.5668 ⁇ m
  • the surface roughness of the curved surface obtained by the partition processing of the present invention is 2.7193 ⁇ m, which is 23.76% lower than that of the overall processing.
  • the results are shown in FIG. 5a) represents the roughness of the processed surface using the conventional integral processing method
  • FIG. 5b) represents the roughness of the processed surface using the partitioned processing method of the present invention.
  • the profile of the curved surface obtained by the traditional overall processing is 153.6 ⁇ m
  • the profile of the curved surface obtained by the partition processing of the present invention is 91.84 ⁇ m, which is 40.21% lower than that of the overall processing.
  • the results are shown in FIG. 6.

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Abstract

提供了一种基于矢量场的曲面分区加工轨迹拓扑形状设计方法。该方法分别建立弦高/残高误差与走刀方向法曲率的函数关系，经归一化构建双目标优化模型，通过评价函数求解各点最优走刀方向，建立空间矢量场；计算投影后平面矢量场散度与旋度，根据其是否为零实现加工区域初分割；分析不同矢量场特征，拟合空间矢量场流线，计算机床旋转轴沿流线进给运动的运动学参数，根据其是否突变完成加工区域细分；结合走刀方式实现曲面不同加工区域加工轨迹拓扑形状设计。该方法适用于复杂曲面分区加工，可减小加工误差，提高进给运动平稳性。

Description

基于矢量场的曲面分区加工轨迹拓扑形状设计方法 技术领域
本发明属于复杂曲面零件高精高效铣削加工技术领域，涉及一种基于矢量场的曲面分区加工轨迹拓扑形状设计方法。
背景技术
当前，航空航天、能源动力、汽车船舶等领域的发展对复杂曲面零件的加工精度提出了极高的要求，传统采用统一工艺全域加工的方法适用度降低，易导致误差分布不均及局部超差，难以适用于复杂曲面零件高精度加工。为满足此类零件的加工要求，常采用分区加工方法，将复杂曲面划分成多个加工区域，对不同加工区域分别进行适宜的加工轨迹及加工工艺规划。传统分区方法多围绕曲面曲率、法向量等制定分区准则，其分区结果对于避免加工干涉与提高加工效率等方面具有一定的指导意义。然而，现有分区准则仅针对曲面几何特征，缺乏对加工走刀方式与加工过程中进给运动平稳性的综合考虑，且加工区域分割与轨迹规划相互独立，不同加工区域的加工轨迹拓扑形状设计缺乏理论依据，易诱发局部误差超差及显著切削振动，严重制约曲面加工质量的全面提高。由此，迫切需要研究一种基于矢量场的曲面分区加工轨迹拓扑形状设计方法，以满足复杂曲面零件分区加工的高精度加工要求。
郝小忠等人的专利“考虑误差区域性分布的数控加工刀轨分区映射方法”，公开号CN107145126A。该专利根据工件理论面生成理论刀轨，将工件实际面与理论面对比得到误差分布规律，根据误差分布规律对实际面进行区域划分，针对不同误差类型的区域选择相应的刀轨映射方法将理论刀轨映射到工件实际面上完成刀轨映射过程。然而，该方法的分区结果易受测量误差的影响，且分区过程中实际面与理论面的对比方法缺乏理论支撑，因此该分区方法具有较大局限性。Tuong等人的文献“A practical approach for partitioning free-form surfaces”，International Journal of Computer Integrated Manufacturing，2010，23(11)，992-1001，提出了一种基于曲面曲率的复杂曲面分区方法。该方法通过计算曲面各点的高斯曲率和平均曲率，将加工区域划分为凹区、凸区及鞍区，并对不同区域规划不同加工工艺，实现了加工效率的大幅度提高。然而，该方法未考虑加工过程中进给运动平稳性，加工轨迹拓扑形状设计缺乏理论依据，具有一定的局限性。
发明内容
本发明针对现有技术缺陷，提出一种基于矢量场的曲面分区加工轨迹拓扑形状设计方法。针对复杂曲面分区加工过程中，加工区域分割与轨迹规划缺乏对走刀方式与进给运动平稳性综合考虑，造成的局部误差超差及显著切削振动等问题，通过建立弦高误差与残高误差协同约束的走刀矢量场，实现基于走刀矢量分布的加工区域初分割及确保进给运动平稳的加工区 域细分，根据分区结果，最终完成复杂曲面零件分区加工轨迹拓扑形状设计。由此有效提高了曲面分区加工的加工精度及进给运动的平稳性，为复杂曲面高精高效加工提供技术支撑。
本发明的技术方案是一种基于矢量场的曲面分区加工轨迹拓扑形状设计方法，其特征在于，该方法分别建立弦高/残高误差与走刀方向法曲率的函数关系，即弦高误差与残高误差协同约束的走刀矢量场，经归一化构建两类误差的双目标优化模型，通过构造评价函数求解各点最优走刀方向，建立空间矢量场；计算投影后平面矢量场散度与旋度，根据其是否为零对矢量场分类，实现加工区域初分割；分析不同矢量场特征，拟合空间矢量场流线，计算机床旋转轴沿流线进给运动的运动学参数，根据其是否突变完成加工区域细分；结合走刀方式，实现曲面不同加工区域加工轨迹拓扑形状设计；方法的具体步骤如下：
步骤1，建立弦高误差与残高误差协同约束的走刀矢量场
取空间直角坐标系O-xyz中的曲面加工区域为S(u,v)＝(x(u,v),y(u,v),z(u,v))，其中u和v为曲面参数；在行距d与步长f确定时，曲面加工轨迹上任意一点处弦高误差e计算为：
Figure PCTCN2019101266-appb-000001
其中，k f为走刀方向法曲率。
取变量e *计算为：
e *＝k f 2  (2)
分别求解弦高误差e与变量e *的单调性知，两者呈正相关关系，为降低后续计算难度，使用变量e *表示弦高误差。
残高误差h计算为：
Figure PCTCN2019101266-appb-000002
其中，k d为行距方向法曲率，r为刀具有效半径。
由微分几何知，行距方向与走刀方向互相垂直，满足式(4)：
k d+k f＝2H  (4)
其中，H为平均曲率，对于曲面任意一点，H为定值。
联立式(3)-(4)，残高误差表示为：
Figure PCTCN2019101266-appb-000003
由式(2)与式(5)知，步长及行距确定时，弦高误差与残高误差仅由走刀方向法曲率决定。为求解各点最优走刀方向，以两类误差为目标函数构造双目标优化模型。
对两类误差归一化处理为：
Figure PCTCN2019101266-appb-000004
其中，e n和h n分别表示归一化的弦高误差和残高误差，
Figure PCTCN2019101266-appb-000005
和
Figure PCTCN2019101266-appb-000006
表示弦高误差的最小值和最大值，h min和h max表示残高误差的最小值和最大值，其求解如下：
以k 1和k 2表示曲面主曲率(k 1＞k 2)，其计算为：
Figure PCTCN2019101266-appb-000007
其中，K为高斯曲率，对于曲面任意一点，K为定值。
由式(2)与式(5)得，残高误差的最值为：
Figure PCTCN2019101266-appb-000008
弦高误差的最大值为：
Figure PCTCN2019101266-appb-000009
弦高误差的最小值为：
Figure PCTCN2019101266-appb-000010
根据式(6)-(10)得，归一化的残高误差h n为：
Figure PCTCN2019101266-appb-000011
归一化的弦高误差e n为：
Figure PCTCN2019101266-appb-000012
为方便描述，后文出现的弦高误差与残高误差均为归一化的弦高误差与残高误差，以两类误差为目标函数建立双目标优化模型为：
Figure PCTCN2019101266-appb-000013
式中，V-min表示向量极小化，即向量目标中的e n和h n两个子目标函数都尽可能小；
运用线性加权法构造评价函数Q为：
Figure PCTCN2019101266-appb-000014
其中，α 1和α 2分别为弦高误差和残高误差在评价函数中所占权重，其计算如下：
Figure PCTCN2019101266-appb-000015
其中，h n1为弦高误差取最小值时对应的残高误差，e n1为残高误差取最小值时对应的弦高误差，h nmin为残高误差最小值，e nmin为弦高误差最小值。
根据主曲率取值范围，计算双目标优化模型最优解如下：
(1)当k 2≥0时，取k f＝k 2，e n和h n均取得最小值，因而，k f＝k 2为双目标优化模型最优解，由欧拉定理知：
k f＝k 1cos 2θ+k 2sin 2θ  (16)
其中，θ为走刀方向与k 1对应主方向的夹角，此时，
Figure PCTCN2019101266-appb-000016
(2)当-k 1≤k 2＜0时，评价函数Q为：
Figure PCTCN2019101266-appb-000017
取
Figure PCTCN2019101266-appb-000018
Q取得最小值，因而，
Figure PCTCN2019101266-appb-000019
为双目标优化模型最优解，此时，
Figure PCTCN2019101266-appb-000020
(3)当0≤k 1＜-k 2时，评价函数Q为：
Figure PCTCN2019101266-appb-000021
取
Figure PCTCN2019101266-appb-000022
Q取得最小值，因而，
Figure PCTCN2019101266-appb-000023
为双目标优化模型最优解，此时，
Figure PCTCN2019101266-appb-000024
(4)当k 1＜0时，评价函数Q为：
Figure PCTCN2019101266-appb-000025
取
Figure PCTCN2019101266-appb-000026
Q取得最小值，因而，
Figure PCTCN2019101266-appb-000027
为双目标优化模型最优解，此时，
Figure PCTCN2019101266-appb-000028
以(du:dv)表示曲面任意切方向，沿该方向的曲面第一基本形式I和第二基本形式II分别为：
Figure PCTCN2019101266-appb-000029
其中，E、F、G为曲面第一类基本量，L、M、N为曲面第二类基本量，表达如下：
Figure PCTCN2019101266-appb-000030
其中，S u、S v为曲面S(u,v)的一阶偏导数，S uu、S uv、S vv为曲面S(u,v)的二阶偏导数，n为曲面S(u,v)的法向量。
以(du 1:dv 1)表示主曲率k 1对应主方向，其计算为：
Figure PCTCN2019101266-appb-000031
以(du *:dv *)表示最优走刀方向，其计算为：
Figure PCTCN2019101266-appb-000032
其中，a、b、c分别表示为：
Figure PCTCN2019101266-appb-000033
联立式(22)-(24)，求解获得曲面各点最优走刀方向，沿此方向建立单位走刀矢量，从而形成弦高误差与残高误差协同约束的走刀矢量场。
步骤2，基于走刀矢量分布的加工区域初分割
经步骤1获得的空间走刀矢量场在空间直角坐标系O-xyz中可表示为F(γ)＝(g 1(x,y,z),g 2(x,y,z),g 3(x,y,z))，其中γ为曲面各点沿最优走刀方向的单位走刀矢量。将该矢量场向xOy平面投影，沿各点投影后的走刀方向建立单位走刀矢量γ *，获得平面矢量场A(γ *)＝(f 1(x,y),f 2(x,y))。在复杂曲面生成的走刀矢量场中，走刀矢量分布呈现区域性。针对具有区域性走刀矢量分布的矢量场，开展基于走刀矢量分布的加工区域初分割。
根据矢量场的散度和旋度，可以确定该矢量场内的走刀矢量分布。在平面矢量场A(γ *)＝(f 1(x,y),f 2(x,y))中任意一点的散度divA(γ *)计算为：
Figure PCTCN2019101266-appb-000034
式中，
Figure PCTCN2019101266-appb-000035
为哈密顿算子。
任意一点的旋度rotA(γ *)计算为：
Figure PCTCN2019101266-appb-000036
式中，k为沿空间直角坐标系z轴正向的单位矢量。
计算曲面各点散度和旋度，根据散度和旋度是否为零，将平面矢量场分为以下四类：
(1)无散无旋场
此类平面矢量场散度与旋度均为零，各点走刀矢量分布呈现平行状态。
(2)无散有旋场
此类平面矢量场散度为零，旋度不为零，各点走刀矢量分布呈现涡旋状态。
(3)有散无旋场
此类平面矢量场散度不为零，旋度为零，各点走刀矢量分布呈现辐射状态。
(4)有散有旋场
此类平面矢量场散度与旋度均不为零，各点走刀矢量分布呈现无规则状态。
通过对平面矢量场各点散度与旋度求解，确定不同加工区域对应矢量场类型，将平面矢量场中散度或旋度突变点映射到曲面上，拟合曲线作为不同加工区域的边界，完成基于走刀矢量分布的加工区域初分割。
步骤3，确保进给运动平稳的加工区域细分
结合步骤2的加工区域初分割结果，对不同加工区域的空间矢量场进行流线拟合，根据 机床旋转轴沿矢量场流线进给运动的运动学参数，开展确保进给运动平稳的加工区域细分。
以AC双转台型五轴数控机床为例，其旋转工作台A的转轴与机床坐标系的X轴平行，旋转工作台C的转轴与机床坐标系的Z轴平行。取加工区域空间矢量场的流线为r(ξ)，其中，ξ为流线方程的弧长参数。以曲面上流线处的法向量n(ξ)＝(n x(ξ),n y(ξ),n z(ξ))作为机床旋转轴沿流线进给运动的刀轴矢量，计算为：
Figure PCTCN2019101266-appb-000037
其中，S u(u(ξ),v(ξ))、S v(u(ξ),v(ξ))为曲面S(u,v)在流线处的一阶偏导数。
根据流线上各点刀轴矢量，求解机床A、C轴转角β A(ξ)、β C(ξ)分别为：
Figure PCTCN2019101266-appb-000038
结合式(27)-(28)，计算机床A、C轴沿矢量场流线进给运动的角速度ω A(ξ)和ω C(ξ)分别为：
Figure PCTCN2019101266-appb-000039
其中，t表示加工时间，v表示设定的进给速度。
计算机床A、C轴沿矢量场流线进给运动的角加速度α A(ξ)和α C(ξ)分别为：
Figure PCTCN2019101266-appb-000040
由此可得到机床旋转轴沿矢量场流线进给运动的角速度ω(ξ)与角加速度α(ξ)的值为：
Figure PCTCN2019101266-appb-000041
为避免机床旋转轴沿流线进给运动时出现明显切削振动，各加工区域内角速度和角加速度需满足：
Figure PCTCN2019101266-appb-000042
其中，σ表示设定的平稳系数，σ越小则进给运动越平稳，其取值范围一般为1-5，s表示流线总弧长。
根据式(32)对进给运动是否平稳进行判断，以不满足该式的点作为旋转轴角速度或角加速度突变点，在加工区域初分割的基础上，求解得到各加工区域突变点并拟合曲线作为新增分区边界，完成确保进给运动平稳的加工区域细分。
步骤4，曲面不同加工区域加工轨迹拓扑形状设计
通过步骤2与步骤3将复杂曲面分割为走刀矢量分布规则且沿矢量场流线进给运动平稳的不同加工区域，结合走刀方式，对各加工区域进行适宜的加工轨迹拓扑形状设计。
常用走刀方式主要有行切走刀与环切走刀两种，针对不同加工区域对应的平面矢量场类型，分别在不同加工区域对应的平面上设计二维加工轨迹拓扑形状如下：
(1)无散无旋场
此类平面矢量场各点走刀矢量分布呈现平行状态，因此采用行切走刀加工。以各点走刀矢量为加工轨迹切向进行流线拟合，生成平行状的二维加工轨迹。
(2)无散有旋场
此类平面矢量场各点走刀矢量分布呈现涡旋状态，当区域边界曲线与矢量场流线平行时，则流线为完整涡旋线，采用环切走刀加工；当区域边界曲线与矢量场流线不平行时，则流线为局部涡旋线，采用行切走刀加工。以各点走刀矢量为加工轨迹切向进行流线拟合，生成涡旋状的二维加工轨迹。
(3)有散无旋场
此类平面矢量场各点走刀矢量分布呈现辐射状态，因此采用行切走刀加工。以各点走刀矢量为加工轨迹切向进行流线拟合，生成辐射状的二维加工轨迹。
(4)有散有旋场
此类平面矢量场各点走刀矢量分布呈现无规则状态，不宜采用行切或环切走刀加工，因此将有散有旋场转化为无散无旋场，鉴于无散无旋场走刀矢量分布呈现平行状态，故对有散有旋场走刀矢量调整如下：
取有散有旋场B(γ *)＝(f 1(x,y),f 2(x,y))内部m个走刀矢量，分别表示为
Figure PCTCN2019101266-appb-000043
其中i＝1,2,···,m。以走刀矢量平均值
Figure PCTCN2019101266-appb-000044
作为调整后无散无旋场对应的走刀矢量，计算为：
Figure PCTCN2019101266-appb-000045
以各点调整后的走刀矢量为加工轨迹切向进行流线拟合，生成平行状的二维加工轨迹。
在不同加工区域对应的平面上完成二维加工轨迹拓扑形状设计后，将二维加工轨迹映射到曲面上获得三维加工轨迹，从而实现基于矢量场的曲面分区加工轨迹拓扑形状设计。
本发明的显著效果和益处是提出了一种基于矢量场的曲面分区加工轨迹拓扑形状设计方法，该方法针对复杂曲面分区加工过程中，加工区域分割与轨迹规划缺乏对走刀方式与进给运动平稳性综合考虑造成的局部误差超差及显著切削振动等问题，通过建立弦高误差与残高误差协同约束的走刀矢量场，完成基于走刀矢量分布的加工区域初分割及确保进给运动平稳的加工区域细分，并最终实现复杂曲面零件分区加工轨迹拓扑形状设计，有效减小了曲面分区加工的加工误差，提高了进给运动的平稳性，为复杂曲面高精高效加工提供技术支撑。
附图说明
图1—方法整体流程图；图2—弦高误差与残高误差协同约束的走刀矢量场；图3—经基于走刀矢量分布的加工区域初分割与确保进给运动平稳的加工区域细分后的曲面分区结果图；图4—单一加工区域设计的加工轨迹拓扑形状；图5—a)表示采用传统整体加工方法的加工表面粗糙度，b)表示采用本发明所述分区加工方法的加工表面粗糙度；Ra表示加工表面粗糙度(μm)；图6—三坐标测量机测量的分别采用传统整体加工方法与本发明所述分区加工方法的加工表面轮廓对比图。
具体实施方式
结合技术方案与附图详细说明本发明的具体实施方式。
复杂曲面分区加工过程中，由于加工区域分割与轨迹规划缺乏对走刀方式与进给运动平稳性的综合考虑，易诱发局部误差超差及显著切削振动，严重影响曲面加工质量。针对这一情况，为了提高曲面分区加工的加工精度及进给运动的平稳性，发明了一种基于矢量场的曲面分区加工轨迹拓扑形状设计方法，整体流程如附图1所示。
实施例采用AC双转台型五轴数控机床，以具有高陡度、频凹凸、曲率突变特征的复杂曲面为例，借助UG软件和MATLAB软件，详细说明本发明实施过程。
首先，利用UG软件对该复杂曲面进行建模，以局部陡度60°的对称回转面为主体，在 该回转面上设计两个不规则凹坑，进而建立具有高陡度、频凹凸、曲率突变特征的复杂曲面，如图3所示。根据式(1)-(5)建立曲面各点弦高/残高误差与走刀方向法曲率/行距方向法曲率的函数关系，经式(6)-(12)完成两类误差的归一化处理，利用MATLAB软件，通过式(13)-(24)构建并求解两类误差的双目标优化模型，获得各点最优走刀方向，进而建立弦高误差与残高误差协同约束的走刀矢量场参见附图2。
其次，对该空间向量场投影获得平面向量场，通过MATLAB软件，由式(25)-(26)计算平面矢量场各点散度与旋度，其中散度的最大值与最小值分别为0.2299和0，旋度的最大值与最小值分别为0.1191和0.0045。根据各点散度和旋度是否为零对平面矢量场进行分类，以散度或旋度突变点拟合的曲线作为分区边界，完成该复杂曲面的加工区域初分割。其中，曲面凹坑部分对应有散有旋场，其余部分对应无散有旋场，
然后，利用MATLAB软件中streamslice函数对不同加工区域的空间矢量场进行流线拟合，通过式(27)-(31)计算机床旋转轴沿流线进给运动的角速度和角加速度，其中曲面凹坑处最大角速度为16.56°/s，最大角加速度为864.29°/s 2。根据式(32)设定平稳系数为2，求解流线上旋转轴角速度或角加速度突变点并拟合曲线作为新增分区边界，完成该复杂曲面的加工区域细分，最终分区结果参见附图3。
最后，结合常见的行切与环切走刀方式，对不同加工区域加工轨迹拓扑形状进行设计，该复杂曲面凹坑处为有散有旋场，根据式(33)调整各点走刀矢量，生成相应的行切加工轨迹参见附图4，其余部分为无散有旋场，综合考虑区域边界与矢量场流线，分别生成相应的行切与环切加工轨迹，完成基于矢量场的曲面分区加工轨迹拓扑形状设计。
为验证此方法的有效性，进行传统整体加工与本发明所述分区加工对比实验。对比实验采用相同的加工工艺参数，分别为主轴转速5000r/min，切深0.25mm，进给速度300mm/min，行距0.2mm，步长1.8mm。实验结果表明，经本发明所述分区加工得到的曲面与经传统整体加工得到的曲面相比，分区加工的加工质量有显著提升。以工件高度40mm处的加工区域为代表，对其表面粗糙度及轮廓度进行测量。经传统整体加工得到的曲面表面粗糙度为3.5668μm，经本发明所述分区加工得到的曲面表面粗糙度为2.7193μm，较整体加工降低了23.76％，所示结果参见附图5，其中，图5a)表示采用传统整体加工方法的加工表面粗糙度，图5b)表示采用本发明所述分区加工方法的加工表面粗糙度。经传统整体加工得到的曲面轮廓度为153.6μm，经本发明所述分区加工得到的曲面轮廓度为91.84μm，较整体加工降低了40.21％，所示结果参见附图6。判定结果与实验结果一致，说明利用本发明的基于矢量场的曲面分区加工轨迹拓扑形状设计方法可有效减小曲面加工的加工误差，提高复杂曲面零件的加工质量，对工程实际中的加工轨迹规划具有重要的指导作用。

Claims (1)

  1. 一种基于矢量场的曲面分区加工轨迹拓扑形状设计方法，其特征是，该方法分别建立弦高/残高误差与走刀方向法曲率的函数关系，即弦高误差与残高误差协同约束的走刀矢量场，经归一化构建两类误差的双目标优化模型，通过构造评价函数求解各点最优走刀方向，建立空间矢量场；计算投影后平面矢量场散度与旋度，根据其是否为零对矢量场分类，实现加工区域初分割；分析不同矢量场特征，拟合空间矢量场流线，计算机床旋转轴沿流线进给运动的运动学参数，根据其是否突变完成加工区域细分；结合走刀方式，实现曲面不同加工区域加工轨迹拓扑形状设计；方法的具体步骤如下：
    步骤1，建立弦高误差与残高误差协同约束的走刀矢量场
    取空间直角坐标系O-xyz中的曲面加工区域为S(u,v)＝(x(u,v),y(u,v),z(u,v))，其中u和v为曲面参数；在行距d与步长f确定时，曲面加工轨迹上任意一点处弦高误差e计算为：
    Figure PCTCN2019101266-appb-100001
    其中，k f为走刀方向法曲率；
    取变量e *计算为：
    e *＝k f 2 (2)
    分别求解弦高误差e与变量e *的单调性知，两者呈正相关关系，为降低后续计算难度，使用变量e *表示弦高误差；
    残高误差h计算为：
    Figure PCTCN2019101266-appb-100002
    其中，k d为行距方向法曲率，r为刀具有效半径；
    由微分几何知，行距方向与走刀方向互相垂直，满足式(4)：
    k d+k f＝2H (4)
    其中，H为平均曲率，对于曲面任意一点，H为定值；
    联立式(3)-(4)，残高误差表示为：
    Figure PCTCN2019101266-appb-100003
    由式(2)与式(5)知，步长及行距确定时，弦高误差与残高误差仅由走刀方向法曲率决定；为求解各点最优走刀方向，以两类误差为目标函数构造双目标优化模型；
    对两类误差归一化处理为：
    Figure PCTCN2019101266-appb-100004
    其中，e n和h n分别表示归一化的弦高误差和残高误差，
    Figure PCTCN2019101266-appb-100005
    和
    Figure PCTCN2019101266-appb-100006
    表示弦高误差的最小值和最大值，h min和h max表示残高误差的最小值和最大值，其求解如下：
    以k 1和k 2表示曲面主曲率，k 1＞k 2，其计算为：
    Figure PCTCN2019101266-appb-100007
    其中，K为高斯曲率，对于曲面任意一点，K为定值；
    由式(2)与式(5)得，残高误差的最值为：
    Figure PCTCN2019101266-appb-100008
    弦高误差的最大值为：
    Figure PCTCN2019101266-appb-100009
    弦高误差的最小值为：
    Figure PCTCN2019101266-appb-100010
    根据式(6)-(10)得，归一化的残高误差h n为：
    Figure PCTCN2019101266-appb-100011
    归一化的弦高误差e n为：
    Figure PCTCN2019101266-appb-100012
    弦高误差与残高误差均为归一化的弦高误差与残高误差，以两类误差为目标函数建立双目标优化模型为：
    Figure PCTCN2019101266-appb-100013
    式中，V-min表示向量极小化；
    用线性加权法构造评价函数Q为：
    Figure PCTCN2019101266-appb-100014
    其中，α 1和α 2分别为弦高误差和残高误差在评价函数中所占权重，其计算如下：
    Figure PCTCN2019101266-appb-100015
    其中，h n1为弦高误差取最小值时对应的残高误差，e n1为残高误差取最小值时对应的弦高误差，h n min为残高误差最小值，e n min为弦高误差最小值；
    根据主曲率取值范围，计算双目标优化模型最优解如下：
    (1)当k 2≥0时，取k f＝k 2，e n和h n均取得最小值，因而，k f＝k 2为双目标优化模型最优解，由欧拉定理知：
    k f＝k 1cos 2θ+k 2sin 2θ(16)
    其中，θ为走刀方向与k 1对应主方向的夹角，此时，
    Figure PCTCN2019101266-appb-100016
    (2)当-k 1≤k 2＜0时，评价函数Q为：
    Figure PCTCN2019101266-appb-100017
    取
    Figure PCTCN2019101266-appb-100018
    Q取得最小值，因而，
    Figure PCTCN2019101266-appb-100019
    为双目标优化模型最优解，此时，
    Figure PCTCN2019101266-appb-100020
    (3)当0≤k 1＜-k 2时，评价函数Q为：
    Figure PCTCN2019101266-appb-100021
    取
    Figure PCTCN2019101266-appb-100022
    Q取得最小值，因而，
    Figure PCTCN2019101266-appb-100023
    为双目标优化模型最优解，此时，
    Figure PCTCN2019101266-appb-100024
    (4)当k 1＜0时，评价函数Q为：
    Figure PCTCN2019101266-appb-100025
    取
    Figure PCTCN2019101266-appb-100026
    Q取得最小值，因而，
    Figure PCTCN2019101266-appb-100027
    为双目标优化模型最优解，此时，
    Figure PCTCN2019101266-appb-100028
    以(du:dv)表示曲面任意切方向，沿该方向的曲面第一基本形式I和第二基本形式II分别为：
    Figure PCTCN2019101266-appb-100029
    其中，E、F、G为曲面第一类基本量，L、M、N为曲面第二类基本量，表达式如下：
    Figure PCTCN2019101266-appb-100030
    其中，S u、S v为曲面S(u,v)的一阶偏导数，S uu、S uv、S vv为曲面S(u,v)的二阶偏导数，n为曲面S(u,v)的法向量；
    以(du 1:dv 1)表示主曲率k 1对应主方向，其计算为：
    Figure PCTCN2019101266-appb-100031
    以(du *:dv *)表示最优走刀方向，其计算为：
    Figure PCTCN2019101266-appb-100032
    其中，a、b、c分别表示为：
    Figure PCTCN2019101266-appb-100033
    联立式(22)-(24)，求解获得曲面各点最优走刀方向，沿此方向建立单位走刀矢量，从而形成弦高误差与残高误差协同约束的走刀矢量场；
    步骤2，基于走刀矢量分布的加工区域初分割
    经步骤1获得的空间走刀矢量场在空间直角坐标系O-xyz中表示为F(γ)＝(g 1(x,y,z),g 2(x,y,z),g 3(x,y,z))，其中γ为曲面各点沿最优走刀方向的单位走刀矢量；将该矢量场向xOy平面投影，沿各点投影后的走刀方向建立单位走刀矢量γ *，获得平面矢量场A(γ *)＝(f 1(x,y),f 2(x,y))；在复杂曲面生成的走刀矢量场中，走刀矢量分布呈现区域性；针对具有区域性走刀矢量分布的矢量场，开展基于走刀矢量分布的加工区域初分割；
    根据矢量场的散度和旋度，可以确定该矢量场内的走刀矢量分布；在平面矢量场A(γ *)＝(f 1(x,y),f 2(x,y))中任意一点的散度divA(γ *)计算为：
    Figure PCTCN2019101266-appb-100034
    式中，
    Figure PCTCN2019101266-appb-100035
    为哈密顿算子；
    任意一点的旋度rotA(γ *)计算为：
    Figure PCTCN2019101266-appb-100036
    式中，k为沿空间直角坐标系z轴正向的单位矢量；
    计算曲面各点散度和旋度，根据散度和旋度是否为零，将平面矢量场分为以下四类：
    (1)无散无旋场
    此类平面矢量场散度与旋度均为零，各点走刀矢量分布呈现平行状态；
    (2)无散有旋场
    此类平面矢量场散度为零，旋度不为零，各点走刀矢量分布呈现涡旋状态；
    (3)有散无旋场
    此类平面矢量场散度不为零，旋度为零，各点走刀矢量分布呈现辐射状态；
    (4)有散有旋场
    此类平面矢量场散度与旋度均不为零，各点走刀矢量分布呈现无规则状态；
    通过对平面矢量场各点散度与旋度求解，确定不同加工区域对应矢量场类型，将平面矢量场中散度或旋度突变点映射到曲面上，拟合曲线作为不同加工区域的边界，完成基于走刀 矢量分布的加工区域初分割；
    步骤3，确保进给运动平稳的加工区域细分
    结合步骤2的加工区域初分割结果，对不同加工区域的空间矢量场进行流线拟合，根据机床旋转轴沿矢量场流线进给运动的运动学参数，开展确保进给运动平稳的加工区域细分；
    采用AC双转台型五轴数控机床，其旋转工作台A的转轴与机床坐标系的X轴平行，旋转工作台C的转轴与机床坐标系的Z轴平行；取加工区域空间矢量场的流线为r(ξ)，其中，ξ为流线方程的弧长参数；以曲面上流线处的法向量n(ξ)＝(n x(ξ),n y(ξ),n z(ξ))作为机床旋转轴沿流线进给运动的刀轴矢量，计算为：
    Figure PCTCN2019101266-appb-100037
    其中，S u(u(ξ),v(ξ))、S v(u(ξ),v(ξ))为曲面S(u,v)在流线处的一阶偏导数；
    根据流线上各点刀轴矢量，求解机床A、C轴转角β A(ξ)、β C(ξ)分别为：
    Figure PCTCN2019101266-appb-100038
    结合式(27)-(28)，计算机床A、C轴沿矢量场流线进给运动的角速度ω A(ξ)和ω C(ξ)分别为：
    Figure PCTCN2019101266-appb-100039
    其中，t表示加工时间，v表示设定的进给速度；
    计算机床A、C轴沿矢量场流线进给运动的角加速度α A(ξ)和α C(ξ)分别为：
    Figure PCTCN2019101266-appb-100040
    由此得到机床旋转轴沿矢量场流线进给运动的角速度ω(ξ)与角加速度α(ξ)的值为：
    Figure PCTCN2019101266-appb-100041
    为避免机床旋转轴沿流线进给运动时出现明显切削振动，各加工区域内角速度和角加速度需满足：
    Figure PCTCN2019101266-appb-100042
    其中，σ表示设定的平稳系数，σ越小则进给运动越平稳，其取值范围一般为1-5，s表示流线总弧长；
    根据式(32)对进给运动是否平稳进行判断，以不满足该式的点作为旋转轴角速度或角加速度突变点，在加工区域初分割的基础上，求解得到各加工区域突变点并拟合曲线作为新增分区边界，完成确保进给运动平稳的加工区域细分；
    步骤4，曲面不同加工区域加工轨迹拓扑形状设计
    通过步骤2与步骤3将复杂曲面分割为走刀矢量分布规则且沿矢量场流线进给运动平稳的不同加工区域，结合走刀方式，对各加工区域进行适宜的加工轨迹拓扑形状设计；
    常用走刀方式主要有行切走刀与环切走刀两种，针对不同加工区域对应的平面矢量场类型，分别在不同加工区域对应的平面上设计二维加工轨迹拓扑形状如下：
    (1)无散无旋场
    此类平面矢量场各点走刀矢量分布呈现平行状态，因此采用行切走刀加工；以各点走刀矢量为加工轨迹切向进行流线拟合，生成平行状的二维加工轨迹；
    (2)无散有旋场
    此类平面矢量场各点走刀矢量分布呈现涡旋状态，当区域边界曲线与矢量场流线平行时，则流线为完整涡旋线，采用环切走刀加工；当区域边界曲线与矢量场流线不平行时，则流线为局部涡旋线，采用行切走刀加工；以各点走刀矢量为加工轨迹切向进行流线拟合，生成涡旋状的二维加工轨迹；
    (3)有散无旋场
    此类平面矢量场各点走刀矢量分布呈现辐射状态，因此采用行切走刀加工；以各点走刀矢量为加工轨迹切向进行流线拟合，生成辐射状的二维加工轨迹；
    (4)有散有旋场
    此类平面矢量场各点走刀矢量分布呈现无规则状态，不宜采用行切或环切走刀加工，因此将有散有旋场转化为无散无旋场，鉴于无散无旋场走刀矢量分布呈现平行状态，故对有散有旋场走刀矢量调整如下：
    取有散有旋场B(γ *)＝(f 1(x,y),f 2(x,y))内部m个走刀矢量，分别表示为
    Figure PCTCN2019101266-appb-100043
    其中i＝1,2,···,m；以走刀矢量平均值
    Figure PCTCN2019101266-appb-100044
    作为调整后无散无旋场对应的走刀矢量，计算为：
    Figure PCTCN2019101266-appb-100045
    以各点调整后的走刀矢量为加工轨迹切向进行流线拟合，生成平行状的二维加工轨迹；
    在不同加工区域对应的平面上完成二维加工轨迹拓扑形状设计后，将二维加工轨迹映射到曲面上获得三维加工轨迹，从而实现基于矢量场的曲面分区加工轨迹拓扑形状设计。
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Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
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Citations (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20110137463A1 (en) * 2009-12-09 2011-06-09 Gm Global Technology Operations, Inc. Systems and methods associated with handling an object with a gripper
CN104281098A (zh) * 2014-10-27 2015-01-14 南京航空航天大学 一种复杂曲面动态加工特征建模方法
CN106354098A (zh) * 2016-11-04 2017-01-25 大连理工大学 一种nurbs组合曲面上刀具加工轨迹生成方法
JP2017156867A (ja) * 2016-02-29 2017-09-07 株式会社Ihi 素材形状シミュレーション装置、素材形状シミュレーション方法及び三次元織繊維部品製造方法
CN107491034A (zh) * 2017-08-28 2017-12-19 华中科技大学 一种基于协变场泛函的刀轴矢量优化方法
CN107562013A (zh) * 2017-07-24 2018-01-09 大连理工大学 等残余高度的曲面分区变刀具加工轨迹规划方法
CN108628247A (zh) * 2018-02-01 2018-10-09 大连理工大学 基于边界残高约束的曲面分区加工轨迹规划方法
CN109358568A (zh) * 2018-12-17 2019-02-19 大连理工大学 基于矢量场的曲面分区加工轨迹拓扑形状设计方法

Family Cites Families (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US6437823B1 (en) * 1999-04-30 2002-08-20 Microsoft Corporation Method and system for calibrating digital cameras
TWI329246B (en) * 2007-03-23 2010-08-21 Univ Chung Yuan Christian Measuring method and system for cnc machine
US9381643B2 (en) * 2014-07-03 2016-07-05 GM Global Technology Operations LLC Dynamical system-based robot velocity control
CN105867310B (zh) * 2016-04-11 2018-11-02 北京航空航天大学 基于occ实现t样条模型的数控加工方法及系统
CN107145126B (zh) 2017-06-29 2018-01-16 南京航空航天大学 考虑误差区域性分布的数控加工刀轨分区映射方法

Patent Citations (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20110137463A1 (en) * 2009-12-09 2011-06-09 Gm Global Technology Operations, Inc. Systems and methods associated with handling an object with a gripper
CN104281098A (zh) * 2014-10-27 2015-01-14 南京航空航天大学 一种复杂曲面动态加工特征建模方法
JP2017156867A (ja) * 2016-02-29 2017-09-07 株式会社Ihi 素材形状シミュレーション装置、素材形状シミュレーション方法及び三次元織繊維部品製造方法
CN106354098A (zh) * 2016-11-04 2017-01-25 大连理工大学 一种nurbs组合曲面上刀具加工轨迹生成方法
CN107562013A (zh) * 2017-07-24 2018-01-09 大连理工大学 等残余高度的曲面分区变刀具加工轨迹规划方法
CN107491034A (zh) * 2017-08-28 2017-12-19 华中科技大学 一种基于协变场泛函的刀轴矢量优化方法
CN108628247A (zh) * 2018-02-01 2018-10-09 大连理工大学 基于边界残高约束的曲面分区加工轨迹规划方法
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