Tool Path Optimization Research Articles

Minimizing Flute Engagement to Adjust Tool Orientation for Reducing Surface Errors in Five-Axis Ball End Milling Operations

AbstractSurface errors due to force-induced tool and workpiece deflections are one of the major errors in multi-axis machining of parts especially with thin-walled structures. Dominant approaches to reduce these surface errors are re-machining the part, feed scheduling, and tool path modification. These methods are time consuming and computationally costly, and they rely on experimental data which is used in cutting force and deflection predictions. The present paper introduces a pure geometrical approach to reduce surface errors drastically by minimizing the engagement lengths of flutes’ cutting edges when a point on the flute’s cutting edge is in contact with the design surface. The total engagement length of the flutes’ cutting edges when one of them generates a contact point on the workpiece surface is formulated and considered as the minimization objective function of an optimization problem. Tilt and lead angles, which define the tool orientation, are the design variables of the optimization problem subjected to constraints based on the geometrical requirements of the ball end milling process. The optimization problem uses the nominal tool path to generate an optimal tool path with adjusted tool orientations. The presented method is computationally inexpensive and does not need any experimentally calibrated coefficients to predict cutting forces because of the pure geometrical nature of the approach. The method is experimentally validated through five-axis ball end milling experiments in which more than 90% surface error reduction is achieved.

Tool Path Optimization for Robotic Surface Machining by Using Sampling-Based Motion Planning Algorithms

Abstract This paper develops a tool path optimization method for robotic surface machining by sampling-based motion planning algorithms. In the surface machining process, the tool-tip position needs to strictly follow the tool path curve and the posture of the tool axis should be limited in a certain range. But the industrial robot has at least six degrees-of-freedom (Dof) and has redundant Dofs for surface machining. Therefore, the tool motion of surface machining can be optimized using the redundant Dofs considering the tool path constraints and limits of the tool axis orientation. Due to the complexity of the problem, the sampling-based motion planning method has been chosen to find the solution, which randomly explores the configuration space of the robot and generates a discrete path of valid robot state. During the solving process, the joint space of the robot is chosen as the configuration space of the problem and the constraints for the tool-tip following requirements are in the operation space. Combined with general collision checking, the limited region of the tool axis vector is used to verify the state’s validity of the configuration space. In the optimization process, the sum of the path length of each joint of the robot is set as the optimization objective. The algorithm is developed based on the open motion planning library (OMPL), which contains the state-of-the-art sampling-based motion planners. Finally, two examples are used to demonstrate the effiectiveness and optimality of the method.

Stable honeycomb structures and temperature based trajectory optimization for wire-arc additive manufacturing

We consider two mathematical problems that are connected and occur in the layer-wise production process of a workpiece using wire-arc additive manufacturing. As the first task, we consider the automatic construction of a honeycomb structure, given the boundary of a shape of interest. In doing this, we employ Lloyd’s algorithm in two different realizations. For computing the incorporated Voronoi tesselation we consider the use of a Delaunay triangulation or alternatively, the eikonal equation. We compare and modify these approaches with the aim of combining their respective advantages. Then in the second task, to find an optimal tool path guaranteeing minimal production time and high quality of the workpiece, a mixed-integer linear programming problem is derived. The model takes thermal conduction and radiation during the process into account and aims to minimize temperature gradients inside the material. Its solvability for standard mixed-integer solvers is demonstrated on several test-instances. The results are compared with manufactured workpieces.

Ultra-precision machining of a large amplitude umbrella surface based on slow tool servo

Due to its excellent optical performance and system integration property, micro-nano structure function surface has been widely used in optical apparatus and energy collection equipment. But using traditional processing method can’t obtain a mirror-like surface with high form accuracy and low roughness for sake of its complex micro-nano structure. In this paper, a large amplitude umbrella surface is special designed and single point diamond turning (SPDT) technology based on slow tool servo (STS) is used for umbrella surface machining. The tool path generation, tool radius compensation and tool geometry optimization are detailed for fabricating the desired surface. A new method combined with constant angle and analytical mathematical optimization is proposed for tool path optimization. A large amplitude umbrella surface with the maximum amplitude 0.2 mm and period 8 per cycle is designed, and the machining experiment is carried out on Nanoform 250 ultra-precision machine tool. From the form accuracy 1 μm in surface residual error and 279.12 nm in RMS and the surface roughness 230.10 nm in Ra for the machined surface, it can be seen that a large amplitude umbrella surface is easily fabricated by SPDT under STS controlling.

Tool path optimization in complex geometry parts machining process

Cutting tool optimal path-planning calculation in complex geometry components machine processing is considered as optimization problem solving with constraints. Because complexity of mathematical model definition with considering all relevant factors, control algorithm with optimal adaptive regulator based on output parameters polynomial approximation in various modifications is presented.

3D surface representation and trajectory optimization with a learning-based adaptive model predictive controller in incremental forming

Abstract In this work, a novel learning-based on-line adaptive shape predictive model is developed to represent the 3D surface of the formed shape after springback in single point incremental forming (SPIF). The model can be updated in each step to predict the forming shapes in future prediction horizons given a new potential tool path, with on-line collected historic geometrical data and their corresponding tool path in previous steps. Furthermore, this model is incorporated into a sequential coupled constrained model predictive control algorithm (MPC), to optimize the potential step-down and step-over sizes in future steps, to minimize the geometric error of the whole formed part in SPIF. Two different geometric shapes, a benchmark truncated cone (with only convex geometric feature) and a non-convex dog-bone (with varying convex and concave feature), are selected for the experimental testing of the new developed on-line adaptive model predictive control algorithm (AMPC). This paper presents the detailed data acquisition and modelling process, on-line feedback control algorithms and experimental validation. The experimental results indicated that the maximum geometric error in the concerned region for the benchmark truncated cone shape and the complex non-convex dog-bone shape can be successfully decreased from above 1.25 mm without control to below 0.75 mm with the current adaptive MPC controller, which cannot be achieved with our previous non-adaptive MPC controller. This is believed to be the first attempt to incorporate a learning-based nonlinear adaptive predictive model with a model predictive controller for tool path optimization in incremental forming. The adaptive model predictive controller (AMPC) demonstrated in this work may provide a powerful tool for geometric accuracy improvement for production of complex geometric shapes in varying forming conditions in incremental sheet forming in the future.

Toolpath planning for additive manufacturing using sliced model decomposition and metaheuristic algorithms

Fabrication efficiency has long been a challenge for additive manufacturing. Standard toolpath generation processes usually give rise to a significant number of non-productive motions that undermine production efficiency and degrade part quality due to frequent acceleration and deceleration in wasted motions. In this paper, we introduce an optimized toolpath generation process that comprises of decomposition of sliced model and optimization of fabrication sequences to minimize non-productive toolpaths. Unlike standard toolpaths, optimized toolpaths carry out fabrication of multiple objects in a staggered sequence to maximize manufacturing efficiency. To tackle the problem of interference between a printhead and objects due to changes in the fabrication sequence of layered depositions, an algorithm that adaptively determines collision-free heights is developed. Additionally, sliced model decomposition considerably reduces the number of entities for optimization. The computational cost involved in toolpath optimization is independent of slicing interval; therefore, the effectiveness and applicability of the proposed optimization approach are well maintained for small slicing intervals. Benchmarks are analyzed to demonstrate the effectiveness and robustness of the proposed toolpath planning approach, and two physical experiments are carried out using fused deposition modeling (FDM) and direct metal deposition (DMD) technologies. Non-productive toolpaths are reduced remarkably, and the desired fabrication quality is achieved for both non-metal and metal structures.

Research on deformation prediction and error compensation in precision turning of micro-shafts

The precision turning process has attracted enormous interest in the standardized and mass production of micro-shafts because it produces more efficiency and lower cost compared with the electrical-discharge machining method and micro-machining method. However, there are many critical factors that influence the dimensional accuracy of micro-shafts, such as the error of workpiece deformation, cutting force, and tool setting error. In this paper, a novel error compensation method was proposed to improve the dimensional accuracy of micro-shafts manufactured with the conventional precision machine tool, based on the constant force cutting method and tool path planning. Firstly, a cutting force model was established considering the effect of the tool nose radius, and the finite element method was used to simulate the turning process and predict the workpiece deformation. Secondly, an error analysis model was created by taking tool setting error, workpiece deformation error, and multi-process cumulative error into account, and the optimized tool path and cutting parameters were obtained. Finally, a series of turning experiments were carried out to verify the error compensation strategy and the cutting force model. The results show that the dimensional error of the micro-shafts with a large length-diameter ratio (l = 5 mm, d = 0.4 mm) can be reduced by 90% by means of the proposed error compensation strategy. In addition, the maximum prediction error of cutting forces is less than 8.6%, and the effect of cutting parameters on cutting forces can be concluded as “feed rate > depth of cut > spindle speed.”

A prediction method based on the voxel model and the finite cell method for cutting force-induced deformation in the five-axis milling process

When milling a thin-walled workpiece, knowledge of machining error due to the workpiece deformation induced by cutting force is crucial to ensuring the quality of the final machined part. In the current research of deformation prediction, the finite element method (FEM) is the dominant tool for calculating the deformation induced by the cutting force. However, FEM needs tremendous manual effort to generate a mesh of the in-process workpiece (IPW) and cannot be directly applied to discrete structured models such as the voxel or dexel models that are widely used for its advantage on parallel computation. In addition, a very fine mesh is needed for FEM to preserve the geometry of IPW, but it will lead to a huge global stiffness matrix. Therefore, it calls for a new method of fast deformation prediction in the milling of thin-walled workpieces. In this paper, aiming at the fast prediction of the deformation error of five-axis milling directly and efficiently on the voxel model, we present a prediction algorithm based on a combination of the finite cell method (FCM) and the voxel model. Specifically, in this study, a pipeline of FCM combined with the voxel model is specially designed for the efficient analysis of IPW deformation along a continuous tool path in the five-axis milling of thin-walled workpieces. By introducing a technique of partially updating the global stiffness matrix and the cells’ stiffness matrices, the proposed algorithm can tremendously reduce the FCM calculation time per sample point on the tool path, by as much as 19 times in our test examples. Both computer simulation and physical cutting experiments performed by us have convincingly verified the accuracy of the proposed deformation prediction algorithm. To our best knowledge, this is the first work of introducing FCM on the voxel model to the prediction of deformation induced by cutting force in milling problems, which enables customized tool path design and optimization in the five-axis milling of free-form surfaces.

Continuous Eulerian tool path strategies for wire-arc additive manufacturing of rib-web structures with machine-learning-based adaptive void filling

Rib-web structures are used for lightweight design in various applications. The most prominent cases are found in aerospace engineering, where intricate structures are produced by forging and subsequent machining or by machining from solid blocks of material. Due to the large scrap rate involved in conventional manufacturing, rib-web structures are suitable applications for additive manufacturing (AM) processes. Among the AM processes, wire-arc additive manufacturing (WAAM) is highly suitable for rib-web structures due to its high deposition rate and the potential to manufacture large-size parts. In WAAM, the welding strategy greatly influences the properties and quality of deposited parts. With an increasing number of starts and stops, the danger of uneven material build-up and welding defects increases. Unfortunately, most rib-web structures do not represent Eulerian paths, i.e. they cannot be manufactured with a continuous welding motion, in which every edge is visited only once. This study presents a novel strategy for generating optimal tool paths for WAAM of lightweight rib-web structures, mitigating the disadvantages of discontinuous welding paths such as welding defects and uneven build-up. It is shown that doubling the number of welding passes on each edge of the rib-web structure turns non-Eulerian paths into Eulerian paths, which can be welded continuously. When two or more weld beads are deposited on each edge, the vertices of the rib-web structure may suffer from underfilling. It is shown that this can be avoided by a correction strategy, which consists in manufacturing the part once, evaluating the size of voids in the junctions, and computing a correction to deposit the required amount of material into the center of the junction. While this strategy may be used if a single part is considered, it is shown that the tool path correction to be applied to arbitrary junction geometries can be represented by a neural network that is derived from an experimental database consisting of representative junction types. With this approach, paths for any rib-web geometry can be generated, which saves lead time in variant-rich production. The paths proposed in this work avoid non-welding moves and may hence outperform even single weld-bed strategies in terms of welding efficiency.

The Dependence of Actual Laser Cutting Speed on CNC Sheet Equipment on Number of NC Program Commands for Metal Grades 1.0114 and AWAIMg3

One of the complex optimization problems arising in technical applications is the cutting path problem for CNC sheet metal cutting machines. This problem is to optimize the tool path for the CNC technological equipment when cutting a fixed set of parts allocated on sheet metal. The time of cutting process is one of objective functions for the optimization problem. This objective function depends on six parameters of cutting process: 1) cutting speed; 2) lengths of the cutting tool path; 3) speed of idling motion of tool; 4) length of idling motion; 5) number of piercings; 6) time of one piercing. When programming NC program, speed of cutting is defined by the user of the CAM (Computer-Aided-Manufacturing) system and considered as a constant. However, this is actually not the case. Consequently, the problem of exact calculation of objective function is arisen. In order to solve this problem, the correction coefficients for the cutting speed value defined by the user must been calculated. Obviously, these coefficients will vary for different thicknesses and grades of metal. The paper presents the results of investigates, which made it possible to find the functional dependences of the cutting speed for the CNC laser cutting machine (CO2) on the number of NC program commands for the following metal grades: 1.0114 (thickness Δ = 1-10 mm) and AWAIMg3 (Δ = 1-5 mm).The statistical materials of experiments were processed by using software “Mathcad”. The received results show that the actual average value of cutting speed is monotonically decreasing function depended on number of NC program commands. In addition, the calculation of the actual cutting speed provides not only an accurate calculation of the value of the objective function, but also, as a result, the correct finding of the optimal tool path

Improving the machining dynamics performance and efficiency for complex channel part manufacturing by planning the tool orientations and feed rate sequence

Improving the machining dynamics performance and efficiency of machine tools is extremely important to finish the processing of complex channel parts with high quality in a short time. In this paper, a three-step frame is adopted to achieve this goal by planning the tool orientations and feed rate, which includes C-spaces determination, collaborative optimization of toolpath and feed rates, and the adjustment for over-limitation dynamic parameters. Firstly, a conical ball-end cutter is used and the feasible C-spaces computation method is provided based on the envelop theory. Secondly, a multi-objective mathematical model with multi-constraint conditions for optimizing the dynamics performance and machining efficiency is built. Thirdly, the solving algorithms for the model but simplified is designed to generate the optimal toolpath and initial variable feed rate sequence. To design the efficient algorithms, the Closed-region Parametric Encoding (CPE) method for data structure and the Parametric Data Algorithm Design (PDAD) for algorithm design are proposed, which can transform the geometric constraints into the parametric surfaces in C-space and compute with the continuous parameters to implement the adaptive local subdivision. The algorithms can automatically generate the different shape of toolpath curve to obtain better optimization results. Finally, considering the dynamic parameters limitation, an adjustment algorithm is designed to adjust the feed rates for reducing the over-limitation dynamic parameters. At the end of the paper, two sets of comparative experiments are given for verification. The first set experiment shows that our approach can efficiently improve the machining dynamics performance and efficiency for complex channel parts. The second set experiment shows that the solving algorithm designed by the CPE method and PDAD method has the better computation efficiency and optimization effect.

Tool path optimization based on wear prediction in Electric Arc Sweep Machining

Electric arc sweep machining is a novel method for machining open channel by applying electric arc and high pressured gap flushing. In this method, a shaped and non-rotating tool sweeps on the workpiece surface to erode a layer by scanning machining area following a predefined geometric path. In this condition, tool wear changes around the periphery depending on feeding direction. Therefore, a proper tool path planning is a key factor to improve the machining efficiency and quality. To cover this issue, in this research a procedure is proposed for selecting the best tool pathway for groove machining. Tool path planning is based on uniform bottom erosion mechanism during machining which occurs between end surface of tool electrode and workpiece. For this reason, tool wear prediction is carried out theoretically and then, effects of tool pathway on tool erosion are studied. Finally, tool pathway is optimized to get a uniform tool wear and machined surface. Based on tool wear mechanism, material erosion starts from the edge facing the feeding direction and then expands to other regions in the bottom surface of the tool electrode. Therefore, to achieve a uniform tool wear and a smooth surface, tool feeding direction should change in specific moments to transfer tool erosion to other edges. To verify theoretical findings, a set of experiment is conducted. Experimental results show that optimized tool pathway can both improve MRR and reduce TWR efficiently. Moreover, fabricating a groove by implementing proposed pathway strategies can improve machined surface quality by distributing tool wear uniformly.

Switched model predictive path control of incremental sheet forming for parts with varying wall angles

As a promising rapid manufacturing technology, incremental sheet forming (ISF) has been tentatively applied in forming prototype parts in many industries, such as aerospace, automobile etc. One of the problems facing scientists and engineers is that geometric accuracies of the parts formed by typical open-loop ISF processes cannot meet dimensional requirements in industries. To address this problem, linear model predictive control (MPC) approaches have been developed that optimize the ISF tool paths to reduce geometric errors. However, in the ISF process, the geometric response of the formed part relative to the tool perturbation is highly non-linear. Due to model mismatch, existing linear MPC path control approaches have been successfully applied to simple geometries only. In contrast, this paper proposes a generic and systematic tool path control approach for forming parts with varying wall angles which have more complex geometric features. In particular, a Switched MPC framework based on linearizing the non-linear ISF geometry response with linear parameter-varying (LPV) state-space models is developed. Then, optimized tool paths to compensate geometric errors were determined by solving convex optimization problems. Experiments were conducted to validate the performance of the developed control approach. The results show that the developed Switched MPC was able to reduce the maximum geometric error by 72 %, 49 % and 80 % in the wall, conjunction and base zones of the formed “funnel”-shaped part respectively. Compared to the Conventional MPC, the Switched MPC improved the maximum geometric error in the wall zone by 0.21 mm. The Switched MPC control algorithm is then shown to be robust on two other complex shapes with varying wall angles.

Determination of optimal tool path in drilling operation using Modified Shuffled Frog Leaping Algorithm

Determination of optimal tool path in drilling operation using Modified Shuffled Frog Leaping Algorithm

Study on Design and Diamond Turning of Optical Freeform Surface for Progressive Addition Lenses

Optical freeform surface components have attracted much attention due to their high degree of design freedom and small size. However, the design and processing difficulty of such components limit its wide application in optics industry. In recent years, diamond turning has been considered an efficient method for processing optical freeform surfaces, but the research on tool path generation of this processing method is not systematic. Progressive addition lens (PAL) is a typical optical freeform surface and is widely used to correct people’s vision problems. Firstly, this paper introduces a method of designing PAL. Then, an optimized tool path generation method for diamond turning of the optical freeform surface is proposed, the equal angle method is used to select the discrete points, and a tool nose radius compensation method suitable for both slow slide servo (SSS) and fast tool servo (FTS) is adopted. Finally, the turning experiment is carried out with a single point diamond lathe, and a PAL surface with a roughness of 0.087 μm was obtained. The power and astigmatism distributions were measured using a Rotlex freeform verifier to verify the rationality of the optical design.

An error-bounded B-spline curve approximation scheme using dominant points for CNC interpolation of micro-line toolpath

• The bi-chord error test fully considers the geometric properties of the micro-line toolpath. • The bi-chord errors test greatly reduces the impact of noisy points on the number and distribution of the dominant points. • The chord error estimation for the B-spline curve approximation analytically determines whether or not the geometric deviation between the polygon formed by the micro-line toolpath and the initial B-spline curve is under the chord error constraint. This paper presents a unified framework for computing a B-spline curve to approximate the micro-line toolpath within the desired fitting accuracy. First, a bi-chord error test extended from our previous work is proposed to select the dominant points that govern the overall shape of the micro-line toolpath. It fully considers the geometric characteristics of the micro-line toolpath, i.e., the curvature, the curvature variation and the torsion, appropriately determining the distribution of the dominant points. Second, an initial B-spline curve is constructed by the dominant points in the least square sense. The fitting error is unpredictable and uncontrollable. It is classified into two types: (a) the geometric deviations between the vertices of the polygon formed by the data points and the constructed B-spline curve; (b) those between the edges of the polygon and the constructed B-spline curve. Herein, an applicable dominant point insertion is employed to keep the first geometric deviation within the specified tolerance of fitting error. A geometric deviation model extended from our previous work is developed to estimate the second geometric deviation. It can be effectively integrated into global toolpath optimization. Computational results demonstrate that the bi-chord error test applies to both the planar micro-line toolpath and the spatial micro-line toolpath, and it can greatly reduce the number of the control points. Simulation and experimental results demonstrate that the proposed B-spline approximation approach can significantly improve machining efficiency while ensuring the surface quality.

The quality improvement of polymer-surface treatment due to optimal toolpath and cutting parameters

This article discusses the main directions of development in the sphere of polymer edge cutting machining. The authors proposed a special geometry of the cutting tool, as well as the technology for processing the case-shaped part, found on this study.

Tool-Path Problem in Direct Energy Deposition Metal-Additive Manufacturing: Sequence Strategy Generation

The tool-path problem has been extensively studied in manufacturing technologies, as it has a considerable impact on production time. Additive manufacturing is one of these technologies; it takes time to fabricate parts, so the selection of optimal tool-paths is critical. This research analyzes the tool-path problem in the direct energy deposition technology; it introduces the main processes, and analyzes the characteristics of tool-path problem. It explains the approaches applied in the literature to solve the problem; as these are mainly geometric approximations, they are far from optimal. Based on this analysis, this paper introduces a mathematical framework for direct energy deposition and a novel problem called sequence strategy generation. Finally, it solves the problem using a benchmark for several different parts. The results reveal that the approach can be applied to parts with different characteristics, and the solution to the sequence strategy problem can be used to generate tool-paths.

Modeling machining energy consumption including the effect of toolpath

Abstract It's important to accurately and effectively estimate the overall machining energy consumption so as to compare and select the toolpath that uses the least amount of energy. To this end, a framework to model the energy consumption when machining a workpiece is proposed in this paper. This framework consists of a toolpath planning stage and an energy-modeling stage. The proposed framework is demonstrated using a sample workpiece. The results show that the framework is effective in estimating the machining energy consumption and identifying the optimal toolpath. The framework represents an important method for identifying robust decisions for energy efficiency improvement. © 2020 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/by-nc-nd/3.0/ ). Peer-review under responsibility of the scientific committee of the 27th CIRP Life Cycle Engineering (LCE) Conference.