Theoretical and Experimental Research on Error Analysis and Optimization of Tool Path in Fabricating Aspheric Compound Eyes by Precision Micro Milling

Structure design and fabricating methods of three-dimensional （3D） artificial spherical compound eyes have been researched by many scholars. Micro-nano optical manufacturing is mostly used to process 3D artificial compound eyes. However, spherical optical compound eyes are less at optical performance than the eyes of insects, and it is difficult to further improve the imaging quality of compound eyes by means of micro-nano optical manufacturing. In this research, nonhomogeneous aspheric compound eyes （ACEs） are designed and fabricated. The nonhomogeneous aspheric structure is applied to calibrate the spherical aberration. Micro milling with advantages in processing three-dimensional micro structures is adopted to manufacture ACEs. In order to obtain ACEs with high imaging quality, the tool paths are optimized by analyzing the influence factors consisting of interpolation allowable error, scallop height and tool path pattern. In the experiments, two kinds of ACEs are manufactured by micro-milling with different too path patterns and cutting parameter on the miniature precision five-axis milling machine tool. The experimental results indicate that the ACEs of high surface quality can be achieved by circularly milling small micro-lens individually with changeable cutting depth. A prototype of the aspheric compound eye （ACE） with surface roughness （Ra） below 0.12 p.m is obtained with good imaging performance. This research ameliorates the imaging quality of 3D artificial compound eyes, and the proposed method of micro-milling can improve surface processing quality of compound eyes.

Tool Positioning Algorithm Based on Smooth Tool Paths for 5-axis Machining of Sculptured Surfaces

The current research of the 5-axis tool positioning algorithm mainly focuses on searching the local optimal tool position without gouging and interference at a cutter contact（CC） point,while not considering the smoothness and continuity of a whole tool path.When the surface curvature varies significantly,a local abrupt change of tool paths will happen.The abrupt change has a great influence on surface machining quality.In order to keep generated tool paths smooth and continuous,a five-axis tool positioning algorithm based on smooth tool paths is presented.Firstly,the inclination angle,the tilt angle and offset distance of the tool at a CC point are used as design variables,and the machining strip width is used as an objective function,an optimization model of a local tool positioning algorithm is thus established.Then,a vector equation of tool path is derived by using the above optimization model.By analyzing the equation,the main factors affecting the tool path quality are obtained.Finally,a new tool position optimization model is established,and the detailed process of tool position optimization is also given.An experiment is conducted to machine an aircraft turbine blade by using the proposed algorithm on a 5-axis blade grinding machine,and the machined blade surface is measured with a coordinate measuring machine（CMM）.Experimental and measured results show that the proposed algorithm can ensure tool paths are smooth and continuous,improve the tool path quality,avoid the local abrupt change of tool paths,and enhance machining quality and machining efficiency of sculptured surfaces.

TOOL PATH PLANNING USING VORONOI DIAGRAM AND THREE STACKS

Based on the object oriented data structure of Voronoi diagram, the algorithm of the trimmed offset generating and the optimal too l path planning of the pocket machining for multiply connected polygonal domains are studied. The intersection state transition rule is improved in this algorithm. The intersection is between the trimmed offsets and Voronoi polygon. On this basis, the trimmed offset generating and the optimal tool path planning are mad e with three stacks(I stack, C stack and P stack)in different monotonous pouches of Voronoi diagram. At the same time, a merging method of Voronoi diagram an d offsets generating for multiply connected polygonal domains is also presented. The above algorithms have been implemented in NC machining successfully, and the efficiency is fully verified.

TOOL PATH GENERATION BASED ON STL FILE FOR SHEET METAL DIELESS FORMING

Sheet metal dieless forming is a new metal forming technology. Thistechnology adopts the principle of rapid prototyping technology, so it can form sheet metal partswithout traditional die and moulds. According to the characteristic of sheet metal dieless formingtechnology a new way of tool path generation based on the STL file for sheet metal dieless formingis proposed.

A new iso-scallop height tool path planning method in three-dimensional space

This paper presents a new approach for designing the tool paths in the machining of sculptured surfaces for computer nu- merical controlled end milling. In the proposed method, the tool paths are determined so that the scallop height formed by two adja- cent machining paths is maintained constant across the machined surface. Unlike previous work on iso-scallop height milling, the present work considers the true 3D configuration of the milling procedure and can be used to generate better results, which is shown by examoles.

Tool path generation of ultra-precision diamond turning: A state-of-the-art review

With the increasing market demand for optical complex surface parts,the application of multi-axis ultraprecision single-point diamond turning is increasing.A tool path generation method is very important to decrease manufacturing time,enhance surface quality,and reduce cost.Compared with the tool path generation of the traditional multi-axis milling,that of the ultra-precision single-point diamond turning requires higher calculation accuracy and efficiency.This paper reviews the tool path generation of ultra-precision diamond turning,considering several key issues:cutter location(CL)points calculation,the topological form of tool path,interpolation mode,and G code optimization.

Tool path generation and optimization for freeform surface diamond turning based on an independently controlled fast tool servo

Diamond turning based on a fast tool servo(FTS)is widely used in freeform optics fabrication due to its high accuracy and machining efficiency.As a new trend,recently developed high-frequency and long-stroke FTS units are independently driven by a separate control system from the machine tool controller.However,the tool path generation strategy for the independently controlled FTS is far from complete.This study aims to establish methods for optimizing tool path for the independent control FTS to reduce form errors in a single step of machining.Different from the conventional integrated FTS control system,where control points are distributed in a spiral pattern,in this study,the tool path for the independent FTS controller is generated by the ring method and the mesh method,respectively.The machined surface profile is predicted by simulation and the parameters for the control point generation are optimized by minimizing the deviation between the predicted and the designed surfaces.To demonstrate the feasibility of the proposed tool path generation strategies,cutting tests of a two-dimensional sinewave and a micro-lens array were conducted and the results were compared.As a result,after tool path optimization,the peak-to-valley form error of the machined surface was reduced from 429 nm to 56 nm for the two-dimensional sinewave by using the ring method,and from 191 nm to 103 nm for the micro-lens array by using the mesh method,respectively.

A Tool Path Re-generation Algorithm for Die & Mold Machining

Facing the challenges of a shorter product design a nd manufacturing lead-time, many mold companies are using 3-D CAD/CAM software s ystems in design and manufacturing. A new product file is often issued to the mo ld design department before it is completely finalized and the design may have t o be iterated many times during the mold design and making processes. In practic e, if a mold has been modified, all the tool paths that cover the modified regio n must be re-generated, no matter how small the modified region may be. With th e available tool path generation systems, if a tool path needs to be re-generat ed, all the cutter location (CL) points must be re-calculated, and none of the original CL points can be re-used. It would require as much time to re-gen erate the modified tool path as in the original case. On the other hand, the mod ified region is usually quite small compared with the entire mold. The complete re-generation process is therefore highly unproductive and time-consuming. This paper proposes an efficient tool path re-generation approach for 3-axis d ie and mold machining. It is assumed in this research that a gouge-free too l path has been generated for the original mold and the same ball end-mill is to be used to generate the tool path for the modified mold. It is shown in th is work that if the boundary of the modified region is interference-free, the a ffected CL points are enclosed by a set of CL points which correspond to the poi nts on the boundary of the modified region. An efficient tool path re-generatio n algorithm was developed in this research. With this algorithm, a closed CL cur ve is first generated from the boundary of the affected region. The CL points fo r the original mold are then analyzed by comparing the x and y values with the b oundary of the affected CL points. If the CL points are not affected by the modi fication, they are output to the new CL file directly. Otherwise, they are remov ed and replaced by the new CL points. The algorithm has been tested using severa l industrial parts, and results show that it is efficient, robust, and the re-g enerated tool path is gouge-free and smooth.

ENVELOPING THEORY BASED METHOD FOR THE DETERMINATION OF PATH INTERVAL AND TOOL PATH OPTIMIZATION FOR SURFACE MACHINING

An enveloping theory based method for the determination of path interval in three axis NC machining of free form surface is presented, and a practical algorithm and the measures for improving the calculating efficiency of the algorithm are given. Not only the given algorithm can be used for ball end cutter, flat end cutter, torus cutter and drum cutter, but also the proposed method can be extended to arbitrary milling cutters. Thus, the problem how to strictly calculate path interval in the occasion of three axis NC machining of free form surfaces with non ball end cutters has been resolved effectively. On this basis, the factors that affect path interval are analyzed, and the methods for optimizing tool path are explored.

Global Tool Path Fairing Algorithm for Automated Fiber Placement

A global energy fairing method,applied to automated fiber placement(AFP)tool path,was proposed.The main purpose was to improve the adaptability of AFP path towards part with sharp curvature variation as well as product quality.The relation between path geometric property and manufacturing property was discussed and a series of experiments were carried out.Based on cubic B-Spline global fairing method,the AFP tool path was faired which decreased the tool path curvature and curvature changing rate.Compared with initial ones,the path faired by the proposed method was relatively flat and smooth,which contributed to layup efficiency and reducing bulking defects.The method was demonstrated potentials in application for AFP manufacturing,especially for aeronautic and aerospace industry practice.

A Tool Path Generation Strategy for Sculptured Surfaces Machining

This paper presents a strategy to generate interference-free tool paths for machining sculptured surfaces. The strategy proposed here is first to determine the tool path topology. The values of the step length and the path interval are then calculated based on the machining tolerance requirements. After detecting and eliminating the tool interference, the interference-free tool path is generated. The effectiveness of the developed algorithm is demonstrated through simulation and actual cutting tests.

Generation of tool path for flank milling in divided areas

Presents the division of non developable ruled surface into divided small areas and flank milling in these divided areas to improve machining efficiency and machined surface quality by controlling the machining error for each area, and the algorithms developed for generation of tool path and calculation of errors, and concludes from computer simulation results that the algorithms are correct.

Tool path generation for 5-axis flank milling of ruled surfaces with optimal cutter locations considering multiple geometric constraints

Ruled surfaces found in engineering parts are often blended with a constraint surface,like the blade surface and hub surface of a centrifugal impeller.It is significant to accurately machine these ruled surfaces in flank milling with interference-free and fairing tool path,while current models in fulfilling these goals are complex and rare.In this paper,a tool path planning method with optimal cutter locations(CLs)is proposed for 5-axis flank milling of ruled surfaces under multiple geometric constraints.To be specific,a concise three-point contact tool positioning model is firstly developed for a cylindrical cutter.Different tool orientations arise when varying the three contact positions and a tool orientation pool with acceptable cutter-surface deviation is constructed using a meta-heuristic algorithm.Fairing angular curves are derived from candidates in this pool,and then curve registration for cutter tip point on each determined tool axis is performed in respect of interference avoidance and geometric smoothness.On this basis,an adaptive interval determination model is developed for deviation control of interpolated cutter locations.This model is designed to be independent of the CL optimization process so that multiple CLs can be planned simultaneously with parallel computing technique.Finally,tests are performed on representative surfaces and the results show the method has advantages over previous meta-heuristic tool path planning approaches in both machining accuracy and computation time,and receives the best comprehensive performance compared to other multi-constrained methods when machining an impeller.

Real time tool path smoothing of short linear commands for robot manipulator by constructing asymmetrical Pythagoran-hodograph(PH)splines

Tool path smoothing of linear commands is important to guarantee the high-order motion continuity of multi-axis motion control systems.The existing local tool path smoothing methods mainly construct symmetrical splines at transition corners of linear segments.When the linear segments are short,the symmetrical splines must be shrunk to avoid overlapping,which gives rise to relatively high curvature and low machining efficiency.This paper proposes a tool-path smoothing algorithm for serial industrial robots with 6 rotary(6R)joints by constructing asymmetrical Pythagorean-hodograph(PH)splines.Firstly,symmetrical PH splines are initially constructed at transition corners to realize the third-order differential continuity of tool path position and tool orientation.Tool tip position smoothing errors are constrained by directly evaluating the control polygon length of spline according to the error tolerance in the workpiece coordinate system,while the tool orientation smoothing errors are constrained by adjusting control polygon length after converting tool orientation error to Euler angles using Jacobian matrix.Then asymmetrical splines are constructed by dealing with the spline overlapping problem,while guarantying the fully utilization of error tolerance to reduce spline curvature.The position and orientation are synchronized to the arc-length of the tool tip position to ensure the continuity of acceleration and jerk commands.The control points and arc-length of the constructed asymmetrical splines can all be solved analytically,which makes it suitable for on-line tool path smoothing.Experiments demonstrate that the proposed method achieves higher motion efficiency and lower tracking error than the existing symmetrical and asymmetrical tool path smoothing methods,which validates the advantages of the proposed method in high speed machining.

Improved time-optimal B-spline feedrate scheduling for NURBS tool paths in CNC machining

Feedrate scheduling in computer numerical control(CNC)machining is of great importance to fully develop the capabilities of machine tools while maintaining the motion stability of each actuator.Smooth and time-optimal feedrate scheduling plays a critical role in improving the machining efficiency and precision of complex surfaces considering the irregular curvature characteristics of tool paths and the limited drive capacities of machine tools.This study develops a general feedrate scheduling method for non-uniform rational B-splines(NURBS)tool paths in CNC machining aiming at minimizing the total machining time without sacrificing the smoothness of feed motion.The feedrate profile is represented by a B-spline curve to flexibly adapt to the frequent acceleration and deceleration requirements of machining along complex tool paths.The time-optimal B-spline feedrate is produced by continuously increasing the control points sequentially from zero positions in the bidirectional scanning and sampling processes.The required number of knots for the time-optimal B-spline feedrate can be determined using a progressive knot insertion method.To improve the computational efficiency,the B-spline feedrate profile is divided into a series of independent segments and the computation in each segment can be performed concurrently.The proposed feedrate scheduling method is capable of dealing with not only the geometry constraints but also high-order drive constraints for any complex tool path with little computational overhead.Simulations and machining experiments are conducted to verify the effectiveness and superiorities of the proposed method.

基于OR-Tools的某市高校蔬菜配送路径优化

车辆路径优化问题是运营研究中的一个重要领域,其目的是降低配送成本、提高配送效率。本文以某市高校蔬菜配送车辆路径优化问题为案例,研究如何使用OR-Tools开源软件库来解决这个问题。首先,本文分析了某市高校蔬菜配送车辆的现实需求,包括行驶距离、需求量、车辆容量、数量等参数。在此基础上,建立了一个车辆路径优化模型,旨在最小化车辆总行驶距离或成本,同时满足车辆容量、配送高校顺序等约束条件。其次,使用Python3.8编写代码,借助OR-Tools以及matplotlib分析求解此模型;在求解模型过程中,本文针对某市高校蔬菜配送数据集进行测试。结果表明,其方法能够有效地减少配送车辆的行驶距离和降低配送成本。由此,本文利用OR-Tools软件库成功地研究某市高校蔬菜配送车辆路径优化问题,为实际物流配送提供了有效的决策支持。

Tool Path Generation for Clean-up Machining of Impeller by Point-searching Based Method

Machining quality of clean-up region has a strong influence on the performances of the impeller. In order to plan clean-up tool paths rapidly and obtain good finish surface quality, an efficient and robust tool path generation method is presented, which employs an approach based on point-searching. The clean-up machining mentioned in this paper is pencil-cut and multilayer fillet-cut for a free-form model with a ball-end cutter. For pencil-cut, the cutter center position can be determined via judging whether it satisfies the distance requirement. After the searching direction and the tracing direction have been determined, by employing the point-searching algorithm with the idea of dichotomy, all the cutter contact （CC） points and cutter location （CL） points can be found and the clean-up boundaries can also be defined rapidly. Then the tool path is generated. Based on the main concept of pencil-cut, a multilayer fillet-cut method is proposed, which utilizes a ball-end cutter with its radius less than the design radius of clean-up region. Using a sequence of intermediate virtual cutters to divide the clean-up region into several layers and given a cusp-height tolerance for the final layer, then the tool paths for all layers are calculated. Finally, computer implementation is also presented in this paper, and the result shows that the proposed method is feasible.

Tool path planning based on conformal parameterization for meshes

The similarity property of conformal parameterization makes it able to locally preserve the shapes between a surface and its parameter domain, as opposed to common parameterization methods. A parametric tool path planning method is proposed in this paper through such parameterization of triangular meshes which is furthermore based on the geodesic on meshes. The parameterization has the properties of local similarity and free boundary which are exploited to simplify the formulas for computing path parameters, which play a fundamentally important role in tool path planning, and keep the path boundary-conformed and smooth. Experimental results are given to illustrate the effectiveness of the proposed methods, as well as the error analysis.

An on-line tool path smoothing algorithm for 6R robot manipulator with geometric and dynamic constraints

The tool path smoothness of the industrial robot directly influences the dynamic performance of its motion control. Therefore, it is important to smooth the path that is composed of small linear segments, in order to achieve continuous and smooth movement.This paper uses the FIR filter interpolation method to generate the smooth tool tip position and tool orientation trajectory for robot manipulators with 6 rotational(6R) joints. The geometric smoothness and motion interpolation are achieved in one step.The maximum velocity and acceleration of joints are constrained when calculating the time parameters of the FIR filter. By specially designing the overlapping time at transition corners, the tool tip position and tool orientation deviations are all constrained in the workpiece coordinate system. Considering the complexity of the inverse kinematics of the robot, in order to constrain the velocity and acceleration of robot joints, this paper proposes a simplified method which directly establishes the relationship between joint motion and tool motion through the derivative of joint motion to tool motion without considering the inverse kinematics. Simulation and experiment results show that the algorithm can generate continuous acceleration commands of the tool tip position and tool orientation within the corner error tolerance. The preset velocity and acceleration limitations of six joints are all constrained well. Comparisons with existing algorithms demonstrate advantages of the proposed method.

GENERATE ROUGH TOOL-PATHS FROM UNORGANIZED POINT-CLOUD DIRECTLY

An approach is presented to generate rough interference-free tool-paths directly from massive unorganized data in rough machining that is performed by machining volumes of material in a slice-by-slice manner. Unorganized point-cloud is firstly converted to cross-section data. Then a robust data-structure named tool-path net is constructed to save tool-path data. Optimal algorithms for partitioning sub-cut-areas and computing interference-free cutter-locations are put forward. Finally the tool-paths are linked in a zigzag milling mode, which can be transformed into a traveling sales man problem. The experiment indicates optimal tool paths can be acquired, and high computation efficiency can be obtained and interference can be avoided successfully.