Tool Path Generation Algorithm Research Articles

Fabrication of the freeform Fresnel lens by swinging-rotating diamond ruling

Freeform optics are widely applied across various industries, encompassing both imaging and non-imagining optical systems. To compact the freeform surface, the freeform Fresnel lens has been devised by optical designers. However, conventional slow slide servo techniques cannot effectively fabricate the intricate lens, due to its asymmetry and discontinuity. In this paper, a novel swinging-rotating diamond ruling method is proposed to fabricate a biconical freeform Fresnel lens, with the synchronized motions of X-, Z-, C- and A-axes. The morphed Archimedean driving spiral based on contour lines is constructed to avoid the tool-microstructure interference. The tool path generation algorithm is proposed to generate smooth and accurate tool path, encompassing an adaptive projection principle, a transition tool path interpolation method and a postprocessing method. Finally, the feasibility and superiority of the proposed method is validated through two case studies. It is demonstrated that the precise and efficient fabrication of the freeform Fresnel lens can be realized by swinging-rotating diamond ruling method.

Tool path generation with a uniform residual error distribution considering tool contour error for ultra-precision diamond turning

Tool path generation strategy plays a crucial role in improving the efficiency and surface quality of ultra-precision diamond turning mainly by influencing residual errors. However, current approaches in tool path generation have not achieved a uniform distribution of residual error due to the unexplored and significant impact of tool contour error on residual error. Therefore, this study introduces a novel tool path generation algorithm for ultra-precision diamond turning, aiming for a uniform residual error distribution with consideration of tool contour error. The tool contour is measured off-machine, fitted, and modeled to achieve its actual cutting-edge contour at a submicron scale. An estimation model is established to calculate residual error on the machined surface considering the tool contour error. A tool path generation approach is then proposed to achieve uniform residual error distribution by adaptively controlling stepovers. Then the proposed stepover is smoothed by cubic Hermite polynomial interpolation to avoid undesired tool path fluctuations. To further improve the machining accuracy, a spiral tool path is generated with proper discretization parameters to control chord error. Finally, a prototype software system is developed to optimize the tool path as well as predict the residual and machining error across the entire machined surface. Experiment results demonstrate a significant reduction of approximately 40 % in both residual error and machining error compared to unoptimized results.

Deep reinforcement learning based toolpath generation for thermal uniformity in laser powder bed fusion process

Laser powder bed fusion (LPBF) is a widely used metal additive manufacturing technology. However, the accumulation of internal residual stress during printing can cause significant distortion and potential failure. Although various scan patterns have been studied to reduce possible accumulated stress, such as zigzag scanning vectors with changing directions or a chessboard-based scan pattern with divided small islands, most conventional scan patterns cannot significantly reduce residual stress. The proposed adaptive toolpath generation (ATG) algorithms, aiming to minimize the thermal gradients, may result in extremely accumulated temperature fields in some cases. To address these issues, we developed a deep reinforcement learning (DRL)-based toolpath generation framework, with the goal of achieving uniformly distributed heat and avoiding extremely thermal accumulation regions during the LPBF process. We first developed an overall pipeline for the DRL-based toolpath generation framework, which includes uniformly sampling, agent moving and environment observation, action selection, moving constraints, rewards calculation, and the training process. To accelerate the training process, we simplified the data-intensive numerical model by considering the turning angles on the toolpath. We designed the action spaces with three options, including the minimum temperature value, the smoothest path, and the second smoothest path. The reward function was designed to minimize energy density to ensure the temperature field remains relatively stable. To verify the effectiveness of the proposed DRL-based toolpath generation framework, we performed numerical simulations of polygon shape printing domains. In addition, four groups of thin plate samples with different scan patterns were compared using the LPBF process. The results indicated that using our proposed DRL algorithms for toolpath generation reduced the maximum distortion of the sample by approximate 47% compared to Zigzag patterns, 29% compared to Chessboard patterns, and 17% compared to ATG patterns. Our work demonstrated the effectiveness of implementing machine learning algorithms in the toolpath generation of the LPBF process.

Fabrication of the curved Fresnel lens array on the spherical surface by 6-axis diamond ruling

The curved Fresnel lens array on the spherical surface owns exceptional optical performance and meets the growing demand for smart home and security alarm systems. However, the intricate three-dimensional microstructure of such optical component is typically considered impossible to be directly fabricated by diamond machining. In this paper, a novel 6-axis diamond ruling method is proposed to fabricate the complex optics utilizing a commercial 6-axis ultra-precision machine tool. The kinematic principle and tool path generation algorithm of this method are presented. A varying-angle sampling strategy is employed in the proposed algorithm to reduce the acceleration and following error in the rotation of the A-axis. Novel trial cutting processes are introduced to figure out the tool setting errors induced by visual inspection, which need to be compensated in the tool path. Based on the proposed tool path generation algorithm and cutting processes, this method enables the efficient processing of precise curved Fresnel lenses. There is no interference between the diamond tool and the curved microstructure in the 6-axis synchronized motions. Finally, the feasibility and superiority of this method are experimentally verified by analyzing the surface roughness and shape accuracy of the machined component. It can indeed generate high-quality curved Fresnel lenses on the spherical surface by the proposed 6-axis diamond ruling method.

Implementation and evaluation of curved layer fused deposition modeling

Fused Deposition Modeling (FDM) is an extrusion-based additive manufacturing (AM) process in which a thermoplastic material is extruded through a nozzle. Although it was initially developed for rapid prototyping, advances in the FDM technology have rapidly increased its range of applications. However, the FDM process has inherent disadvantages, such as poor surface finish, severe anisotropic mechanical properties, and increased build time for high-resolution parts. This is the result of the layer-by-layer manufacturing process. To remedy these issues, Curved Layer Fused Deposition Modeling (CLFDM) offers a new building paradigm for FDM in which the material is deposited in curved nonplanar layers. The purpose of this study is to implement a curved-layer toolpath generation algorithm and quantify the benefits of the curved layered methodology over traditional planar layers in printing thin-contoured parts.

Fast tool servo-based ultra-precision diamond sculpturing for fabricating micro-structured surfaces

To eliminate differences in surface quality and improve the machining flexibility of micro-structured surfaces, this paper proposes a novel ultra-precision diamond sculpturing method based on a triaxial fast tool servo (FTS). In this method, the diamond tool is directly driven by the FTS rather than the ultra-precision lathe to fabricate the micro-structure surfaces. The corresponding toolpath generation algorithm is established to take full advantage of the triaxial FTS. The toolpath is first generated through traditional calculating the shortest tool edge projection on the desired surface and the curve interpolation. The overshoot around the path corner is predicted by simulating the tracking path. Then an extended path is added to the original toolpath to stabilize the overshoot before removing the material. The simulation indicates that the hexagonal lens array can be favorably fabricated by the proposed ultra-precision diamond sculpturing method, and the developed toolpath reduces the form error from 20 to 5nm. The sculpturing experiments of sinusoidal micro-structure array and micro-lens array surfaces suggest that their actual peak-to-valley (PV) form errors are 70nm and 50nm, respectively. The single lens with the surface roughness Sa 3.44nm can be precisely fabricated in 0.1s, demonstrating the high machining efficiency and high machining quality of the proposed ultra-precision diamond sculpturing method.

Toolpath Generation Algorithm Using Route Model for Non-planar Layering in Additive Manufacturing

Toolpath Generation Algorithm Using Route Model for Non-planar Layering in Additive Manufacturing

Fabrication of high aspect-ratio aspheric microlens array based on local spiral diamond milling

Ultraprecision mold machining combined with precision glass molding is the most promising technology for the mass production of glass microlens arrays (MLAs). However, fabricating an MLA with a high aspect-ratio (AR) (ratio of height to aperture), submicron scale profile accuracy, nanoscale surface finish, and good consistency remains a considerable challenge. A local spiral diamond milling (LSDM) method is proposed to generate a high AR MLA on a nickel-phosphorous (Ni-P) plated mold. A spiral toolpath generation algorithm that considers the tool edge radius and performs profile error (PV) compensation is developed. Each lenslet at any local position can be precisely machined by controlling the servo motions of the three translational axes. Then, the entire MLA can be generated by shifting the toolpath to go through the centers of all lenslets according to the MLA layout. The tool parameters are optimized to avoid local and global tool interference during machining. The generated toolpath provides steady slide axis movements to avoid dramatic changes in cutting speed and acceleration. An MLA with an AR of 0.166 is fabricated. The results show that the fabricated mold and the molded lenses have a profile accuracy (PV) of less than 1 μm and a surface roughness (Ra) of less than 14 nm. The cross-sectional profiles indicate that the fabricated MLA has high machining consistency.

Minimization of Nonproductive Time in Drilling: A New Tool Path Generation Algorithm for Complex Parts

In computerized tool path programming, the operator/user can generate the tool path based on the shape and geometry of the part to be produced by choosing from a set of predefined strategies available in the library of Computer Aided Manufacturing (CAM) software. These tool paths are typically not optimum, specifically for complex geometries. This paper employed Travelling Salesman Problem (TSP) as a foundation to propose a new tool path optimization algorithm for drilling to minimize the tool path length and subsequently reduce the time spent on nonproductive movements. The proposed algorithm was solved using local search approach in the presence of multiple constraints including geometric obstacles and initial location of tool origin. The outcome was a near-optimum tool path for drilling operations with no collision with workpiece features. The computational efficiency of the proposed algorithm was also compared with other methods in available literature using a standard workpiece as a benchmark. The results confirmed that for given examples, the near-optimum collision-free tool paths using the developed model in this paper were almost 50% shorter than the tool path generated by a commercial CAM software.

A grammar-based algorithm for toolpath generation: Compensating for material deformation in the additive manufacturing of concrete

In architecture, AM technologies have been used for rapid prototyping since the early 1990s. However, using AM for automated building construction represent a revolution for the industry that requires modeling the complex relationships between materials, printing system, and designs. An important aspect of research in this area is the deformation of concrete during printing and how it affects shape accuracy and structural stability of the printed geometries. A previous experimental study proposed a series of equations to predict material deformation for a specific concrete mix. This study incorporates these equations in a shape grammar-based algorithm to decompose complex geometries into simpler ones, slice the simpler geometries, and generate compensated toolpaths. The algorithm was implemented in Grasshopper, a Rhino plugin, and it can be used as a 3D slicer specifically for 3D printing concrete purposes. The slicer is validated with two printing experiments, involving a simple and a complex shape. The algorithm can be extended to other material mixes by developing similar experimental studies and incorporating the resulting equations.

블록 오버랩 기반 CNC의 사이클 타임 예측

This paper proposes a cycle time estimation algorithm of a CNC machine tool, using a block overlap based tool path generation algorithm. Velocity profile generation algorithm of CNC interpolator is proposed to compute the cycle time of the G-Code block. Because the CNC blends adjacent velocity profiles to reduce the cycle time and smooth the tool path, the cycle time is adjusted considering the block overlap. The in-position time of rapid traverse is compensated to improve the cycle time estimation accuracy. The simulation model was designed to estimate the cycle time of the CNC machine tool. A three-axis feed drive testbed was used to evaluate the cycle time estimation accuracy of the proposed algorithm.

Optimisation of tool path shape in trochoidal milling using B-spline curves

In recent years, trochoidal milling has become greatly widespread since it provides high productivity and long tool life, especially when cutting difficult-to-machine materials. Numerous studies have dealt with the analytical description and the experimental investigation of the evolution of cutting force, temperature, tool wear, chatter stability, etc. However, most of these analyses are focusing on the conventional circular and cycloid-shape trajectories. Only a few studies address the potential of improving the efficiency by modifying the tool path shape, leaving significant reserves untapped. If the mathematical formulation of the trajectory cannot be described easily, then a sophisticated optimisation algorithm is needed to determine the appropriate tool path shape. To overcome these difficulties at trochoidal milling of straight slots, the present work proposes a new tool path generation algorithm that can maximize the average material removal rate (MRR) while controlling the tool load. In this approach, the tool path is modelled by a B-spline curve whose control points are optimised using a differential evolution algorithm. The developed tool path generation strategy was compared through simulations and experiments with two widely used solutions viz the traditional cycloid-shaped tool path and a modern approach used in computer-aided manufacturing (CAM) systems. The results reveal that the developed method is able to control the tool load and the smoothness of the tool path, and most importantly, also exceeds the existing methods in terms of productivity.

Digital Programming of Liquid Crystal Elastomers to Achieve High-Fidelity Surface Morphing

Morphable surfaces have the potential to enable new kinds of adaptive systems, but existing fabrication methods have limited ability to achieve high resolution morphing into arbitrarily specified shapes. This work presents a platform and algorithms for toolpath generation to enable freeform structures capable of high-resolution surface morphing. The morphing surfaces were composed of liquid crystal elastomer (LCE), with nematic domains aligned using a scratch post capable of applying adjustable pressure and shear velocity, offering the ability to locally tune actuation strains and thus bending curvature radii from 1.8 mm to 14.4 mm. Patterning toolpaths for multi-layer structures were generated using two alternative algorithms, the results of which were compared using example structures capable of morphing from flat sheets into domes and models of a human faces. This process resulted in morphed human face shapes with structural similarities of up to 84.5% when compared to the original model, demonstrating the high fidelity and reconfigurability of this approach for fabricating complex morphable LCE structures.

Tool Path Generation Algorithm Based on Rough Machining of Jade Carving Surface

To improve the quality of tool paths in surface machining, different machining requirements are considered in the tool path generation algorithm. In the traditional tool path generation algorithm, due to the lack of a unified mathematical calculation framework, these requirements often need to be considered separately, but they often compete with each other, so that different requirements cannot be satisfied at the same time and the tool path cannot achieve the optimal. To resolve this issue, an extensive tool path generation algorithm framework for arbitrary surfaces was proposed. The proposed algorithm transforms the tool path calculation framework into a constrained functional optimization problem by establishing an optimization function based on the potential energy field and an inequality function based on the gradient field in the machining area. By establishing finite element approximation, the functional optimization problem is transformed into a numerical optimization problem, which reduces the difficulty of solving. According to the machining requirements of die surface such as tool path smoothness, line width constraint and cutting direction constraints were transformed into the constraints of potential energy field isopotential line, and the method of generating reciprocating cutter path and cutter contact path isosection cutter path was proposed by optimizing the method. It is evident from the simulation and machining experiments results that continuous and smooth tool paths can be generated by using this algorithm, and machining quality and machining efficiency can be improved. By adding different machining requirements into the framework, a tool path with different optimization objectives can be generated.

Flexible fabrication of Fresnel micro-lens array by off-spindle-axis diamond turning and precision glass molding

Fresnel micro-lens arrays with close-to-wavelength features have significant advantages in minimization of optical systems. However, in the fabrication of a Fresnel micro-lens array by conventional diamond turning, the discontinuous features of the surface profile cause interference between the tool flank face and the finished surface. In this manuscript, a novel off-spindle-axis diamond turning method is proposed to fabricate Fresnel micro-lens array mold insert and a toolpath generation algorithm is developed. The generation of each lenslet is treated as an independent turning operation, and the whole fabrication of a Fresnel micro-lens array is completed by a succession of repetitive turning operations. With this approach, the interference between the tool and the finished surface is avoided, and the form accuracy and surface integrity are improved for each lenslet. Then, the Fresnel micro-lens array mold insert is further utilized in precision glass molding to replicate the micro-lens structures onto transparent polymer substrates. The experimental results indicate that both the diamond-turned and molded Fresnel micro-lens arrays are achieved with homogeneous quality. As an application, a compact imaging system based on the molded Fresnel micro-lens array is demonstrated. The proposed machining method in this study can be employed in the fabrication of Fresnel micro-lens arrays and other micro-optics with discontinuous profiles with high accuracy and machining efficiency.

Curved-layered material extrusion modeling for thin-walled parts by a 5-axis machine

PurposeThe purpose of this paper is to solve the problems of poor mechanical properties, high surface roughness and waste support materials of thin-walled parts fabricated by flat-layered additive manufacturing process.Design/methodology/approachThis paper proposes a curved-layered material extrusion modeling process with a five-axis motion mechanism. This process has advantages of the platform rotating, non-support printing and three-dimensional printing path. First, the authors present a curved-layered algorithm by offsetting the bottom surface into a series of conformal surfaces and a toolpath generation algorithm based on the geodesic distance field in each conformal surface. Second, they introduce a parallel five-axis printing machine consisting of a printing head fixed on a delta-type manipulator and a rotary platform on a spherical parallel machine.FindingsMechanical experiments show the failure force of the five-axis printed samples is 153% higher than that of the three-axis printed samples. Forming experiments show that the surface roughness significantly decreases from 42.09 to 18.31 µm, and in addition, the material consumption reduces by 42.90%. These data indicate the curved-layered algorithm and five-axis motion mechanism in this paper could effectively improve mechanical properties and the surface roughness of thin-walled parts, and realize non-support printing. These methods also have reference value for other additive manufacturing processes.Originality/valuePrevious researchers mostly focus on printing simple shapes such as arch or “T”-like shape. In contrast, this study sets out to explore the algorithm and benefits of modeling thin-walled parts by a five-axis machine. Several validated models would allow comparability in five-axis printing.

RBF Interpolation Algorithm for FTS Tool Path Generation

Freeform optics are defined as nonrotational symmetric optical surfaces in the manufacturing industry. Freeform optics are extensively applied to many areas in order to improve system performance. Fast tool servo (FTS) assisting single-point diamond turning technology has high application prospects in freeform optics machining. This paper discusses the interpolation algorithm for tool path generation of FTS through the application of a radial basis function (RBF) algorithm. For this purpose, a positive definite RBF with compact support was employed as the interpolant. The existence is mathematically proven. Numerical simulations were performed to compare the performances of the RBF algorithm and commonly used algorithms for satisfying the requirements of existence, smoothness, and accuracy. Machining experiments were also conducted to validate the applicability of the algorithm. The simulation results showed that the RBF interpolation algorithm outperformed other algorithms in terms of smoothness. The RBF algorithm also provided the highest interpolation accuracy. Furthermore, the RBF interpolation algorithm exhibited the highest accuracy for error distribution, with large errors distributed mainly in transition areas. The machining results were also in general agreement with the simulation results although obvious practical errors were observed. Overall, RBF interpolation can provide higher accuracy and better smoothness in the tool path generation of FTS.

Reusable support for additive manufacturing

Abstract Additive manufacturing (AM) processes such as material extrusion and vat photopolymerization all require supports to print parts with overhang features. These additional supports using the same or different materials are a waste of materials since they need to be removed after the three-dimensional (3D) printing process and cannot be reused. The printing of supports is also time-consuming for the nozzle-based material extrusion processes. A new type of reusable support has been developed to address the support-related challenges in AM. The main idea is to use a set of dynamically controlled metal pins as a programmable building platform. In the layer fabrication, the metal pins will move up one-layer thickness after the printing of each layer. Also, each metal pin will automatically stop at a specified height that is determined by a combination of metal tubes, magnetic discs, and magnetic rings. Additional supports can be 3D-printed on the top surface of the metal pins, while the amount of the supports is dramatically reduced. After the printing process, the metal rods can be separated from the part and reset for the next printing job. A prototype system has been constructed to demonstrate the reusable support principle. The layout optimization and toolpath generation algorithms for the reusable support are also presented. The experimental results of several test cases show an average of nearly 40% saving on the printing time and material with increased reliability and robustness. The reusable support provides a support generation strategy that could be beneficial to other AM processes such as stereolithography and selective laser melting.

Dynamic reaction of machine tools to transient cutting conditions

Transient machining conditions often occur during the milling process, especially when complex toolpath layouts are deployed. Although modern CAM-aided toolpath generation algorithms aim at keeping the cutter engagement conditions as constant as possible and avoid sudden changes, this can not always be ensured. These transients are accompanied by temporary peak excursions in cutting forces and changing dynamic content of the excitation forces. This may have the potential to excite unwanted vibrations in the machining process and even may initiate chatter. Using a virtual process simulation environment it is possible to predict resultant dynamic forces along a complete NC tool path with high time and angular resolution and gain insights into the dynamics of transient events during machining operations. This simulation environment has the capability to use an analytical cutting force model, which spares extensive testing and parameter identification beforehand. Besides, well known empirical cutting formulations can be used as well. The results of the dynamic force prediction is compared against experimental results for different toolpath layouts and the dynamic behavior of the machine tool under cutting conditions will be discussed.

T-Spline Surface Toolpath Generation Using Watershed-Based Feature Recognition

The freeform surface is treated as a single machining region for most traditional toolpath generation algorithms. However, due to the complexity of a freeform surface, it is impossible to produce a high-quality surface using one unique machining process. Hence, region-based methods are widely investigated for freeform surface machining to achieve an optimized toolpath. The Non-Uniform Rational B-spline Surface (NURBS) represented freeform surface is not suitable for region-based toolpath generation because of the surface gaps caused by NURBS trimming and merging operations. To solve the limitation of the NURBS, T-spline is proposed with the advantages of being gap-free, having less control points, and local refinement, which is an ideal tool for region-based toolpath generation. Thus, T-spline is introduced to represent a freeform surface for its toolpath generation in the paper. A region-based toolpath generation method for the T-spline surface is proposed based on watershed technology. Firstly, watershed-based feature recognition is presented to divide the T-spline surface into a set of sub-regions. Secondly, the concept of a PolyBoundingBox that consists of a set of minimum bounding boxes is proposed to describe the sub-regions, and Manufacturing-Suitable Regions are constructed with the help of T-spline local refinement and the PolyBoundingBox. In the end, an optimized multi-rectangles toolpath generation algorithm is applied for sub-regions. The proposed method is tested using three synthetic T-spline surfaces, and the comparison results show the advantage in toolpath length and toolpath reversing number.