Freeform Surfaces Research Articles

Additive manufacturing of polyamide 12 bulk structures using directed energy deposition with a thulium laser: Effect of process conditions on morphology and mechanical performance

Laser-based directed energy deposition of polymers (DED-LB/P) is a highly flexible additive manufacturing process capable of fabricating three-dimensional structures with a high degree of customization on free-form surfaces. In this article, the manufacturability of polyamide 12 bulk structures using DED-LB/P in combination with a thulium laser operating at a wavelength of 1.94 μm is investigated for the first time. The typical absorption bands at this wavelength eliminate the need for additives such as carbon-based nanoparticles, which would limit the range of applications. The generated structures were analyzed regarding porosity, thermal behavior, and mechanical properties to evaluate the potential of DED-LB/P with a thulium laser. As a consequence of the evaporation of absorbed moisture or ethanol residues resulting from powder preparation, a thermal pretreatment of the polymer powder reduced the porosity of the DED-LB/P structures to 0.9%. Depending on the processing parameters, the crystallinity of the produced structures ranged from 25.6% to 29.9%. For the tensile tests, the required geometries were milled from the DED-LB/P bulk structures. The results show that an ultimate tensile strength of up to 52 MPa, an elongation at break of up to 58%, and Young's modulus of up to 1590 MPa can be achieved. These remarkable mechanical properties are primarily attributed to the complete melting of the powder particles in DED-LB/P and the improved surface quality resulting from the milling process.

Off-axis freeform optical design for large curved field of view imaging

Recording neuron activities is pivotal for elucidating the functionality of the nervous system. However, the curved cortex surface of experimental mice presents a significant challenge for optical systems, particularly when a larger field of view (FOV) is required. To address this challenge, we have designed an off-axis three-mirror system that incorporates freeform surfaces on both the primary and secondary mirrors. This system achieves a large imaging FOV of 18°×9°, delivering near-diffraction-limit imaging quality across a curvature spectrum of −14.7 to −15.3mm. A manufacturability analysis indicates that the freeform surfaces are straightforward to produce, and the overall system demonstrates low sensitivity to tolerance and measurement errors. This study introduces a novel, to the best of our knowledge, solution to the field curvature constraints in optical imaging of cortical activity, providing substantial technical support for in vivo neuronal imaging endeavors.

7-axis synchronization-integrated on-the-fly laser texturing system of freeform surface: Design and development

Abstract While laser surface texturing (LST) is a promising manufacturing technique for surface functionalization, simultaneously realizing high precision and high efficiency in the LST of complex curved surface is challenging, due to continuously varied geometries of laser-matter incidence. In the present work, we propose a novel manufacturing system of 7-axis on-the-fly LST for complex curved surface, based on the integrated synchronization of 5-axis linkage motion platform with 2-axis galvanometer. Specifically, the algorithm for decomposing spatial texture trajectory on curved surface into low-frequency and high-frequency parts is established, based on which the kinematic model of synchronized 7-axis system is developed to derive the motion of each axis in both 5-axis linkage motion platform and 2-axis galvanometer simultaneously. Subsequently, the synchronized 7-axis LST system is experimentally realized, including the setup of mechanical stages integrated with optical path, the configuration of numerical control unit, and the development of processing software. Finally, case study of 7-axis on-the-fly LST of freeform aluminum surface is performed, and the advantages in terms of processing efficiency and texturing accuracy over 5-axis linkage LST are demonstrated. The correlation of reduced following errors between mechanical stages with the promoted performance of curved surface texturing by the 7-axis on-the-fly LST is further analyzed. Current work provides a feasible solution for establishing the manufacturing system for high performance LST of complex curved surface.

Hybrid Refractive and Diffractive Testing Method for Free-Form Convex Mirror in High-Resolution Remote-Sensing Cameras

The development of high-resolution and large field of view remote-sensing cameras is inextricably linked to the application of free-form mirrors. The free-form mirror offers higher design of freedom and is more effective at correcting aberrations in optical systems. The surface shape error of a free-form mirror directly affects the imaging quality of remote-sensing cameras. Consequently, a high-precision free-form mirror detection method is of paramount importance. For the convex free-form surface mirror with a large aperture, a hybrid refractive and diffractive testing method combining computer-generated holography (CGH) and spherical mirrors for high-precision null test is proposed in this paper. When comparing the effect of error and the detection sensitivity of different designs, the results showed that the influence of the system error is reduced by about 42% and the sensitivity is increased by more than 2.6 times. The proposed method can achieve higher testing accuracy and represents an effective and feasible approach for the surface shape detection method.

Improving neural-network-based prediction models for misalignment in off-axis three-mirror anastigmat telescopes

The performance of a telescope system heavily relies on the precise alignment of the mirrors. The off-axis three-mirror anastigmat (TMA) telescope presents unique challenges due to its complex optical design. Each optical element within the off-axis TMA telescope is inherently introduced with theoretical eccentricity and tilt. Furthermore, the incorporation of freeform surfaces and other optical elements with intricate surface features typically leads to low initial alignment accuracy of the optical path. With this low initial alignment accuracy and the noise of the measurements, the prediction of the misalignment of the telescope is getting harder. A fully connected neural network architecture is proposed as a misalignment calculation method for an off-axis TMA telescope system with a freeform surface. Random training data is created by using optical design software. The sensitivity of the mirrors to the wavefront error is quantified and incorporated into the loss function of the neural network to improve prediction accuracy. Adding the noisy measurement samples to the training data creates a noise-immune neural network model. Simulation results show that our model can successfully predict misalignment of the mirrors with noisy measurement values.

A Study on the Coarse-to-Fine Error Decomposition and Compensation Method of Free-Form Surface Machining

To improve the machining accuracy of free-form surface parts, a coarse-to-fine free-form surface machining error decomposition and compensation method is proposed in this paper. First, the machining error was coarsely decomposed using variational mode decomposition (VMD), and the correlation coefficients between the intrinsic mode function (IMF) and the machining error were obtained to filter out the IMF components that were larger than the thresholding value of the correlation coefficients, which was the coarse systematic error. Second, the coarse systematic errors were finely decomposed using empirical mode decomposition (EMD), which still filters out the IMF components that are larger than the thresholding value of the set correlation coefficient based on the correlation coefficient. Then, the wavelet thresholding method was utilized to finely decompose all the IMF components whose correlation coefficients in the first two decomposition processes were smaller than the threshold value of the correlation coefficient set. The decomposed residual systematic errors were reconstructed with the IMF components screened in the EMD fine decomposition, which gave the fine systematic error. Finally, the machining surface was reconstructed according to the fine systematic error, and its corresponding toolpath was generated to compensate for the machining error without moving the part. The simulation and analysis results of the design show that the method has a more ideal processing error decomposition ability and can decompose the systematic error contained in the processing error in a more complete way. The results of actual machining experiments show that, after using the method proposed in this paper to compensate for the machining error, the maximum absolute machining error decreased from 0.0580 mm to 0.0159 mm, which was a 72.5% reduction, and the average absolute machining error decreased from 0.0472 mm to 0.0059 mm, which was an 87.5% reduction. It was shown that the method was effective and feasible for free-form surface part machining error compensation.

Effect of tool orientation on surface roughness and dimensional accuracy in ball end milling of thin-walled blades

AbstractIn the aerospace industry, high-precision components like impellers and blisks present considerable challenges in machining due to their intricate geometries and the need for reliable performance. Blades, often classified as thin-walled parts with complex, free-form surfaces, are crucial in ensuring the efficiency and safety of aircraft engines. Their geometries and materials require strict control over cutting parameters, such as tool path and orientation, to avoid deformation and maintain surface integrity. This study investigates the impact of tilt angle variation during ball end milling of Ti6Al4V thin-walled parts. Four different tilt angles (15°, 30°, 45°, and 60°) were analysed to evaluate their effect on dimensional accuracy and surface roughness. The results show that tilt angle significantly influences surface quality and dimensional precision. A tilt angle of 30° achieved the best balance between surface finish and dimensional tolerances, with flatness values ranging from 0.038 mm at 30° to 0.101 mm at 60°, representing a 152.5% increase in flatness. The findings provide practical guidelines for optimizing ball end milling of thin-walled components, emphasizing the importance of tool orientation in reducing deformation and enhancing surface quality.

Grid Optimization of Free-Form Spatial Structures Considering the Mechanical Properties

In recent years, the application of free-form surface spatial grid structures in large public buildings has become increasingly common. The layouts of grids are important factors that affect both the mechanical performance and aesthetic appeal of such structures. To achieve a triangular grid with good mechanical performance and uniformity on free-form surfaces, this study proposes a new method called the “strain energy gradient optimization method”. The grid topology is optimized to maximize the overall stiffness, by analyzing the sensitivity of nodal coordinates to the overall strain energy. The results indicate that the overall strain energy of the optimized grid has decreased, indicating an improvement in the structural stiffness. Specifically, compared to the initial grid, the optimized grid has a 30% decrease in strain energy and a 43.3% decrease in maximum nodal displacement. To optimize the smoothness of the grid, the study further applies the Laplacian grid smoothing method. Compared to the mechanically adjusted grid, the structural mechanical performance does not significantly change after smoothing, while the geometric indicators are noticeably improved, with smoother lines and regular shapes. On the other hand, compared to the initial grid, the smoothed grid has a 21.4% decrease in strain energy and a 28.3% decrease in maximum nodal displacement.

Design of geostationary orbit ultrawide FOV long-wave infrared imaging spectrometer

The geostationary orbit imaging spectrometer offers distinct advantages for diverse applications in remote sensing. To enhance swath and data richness, there is a growing trend toward spectrometers with broader fields of view (FOV) and extended slit lengths. Optical systems equipped with these features face significant challenges in aberration correction. This paper investigates the parameters of geostationary orbits and designs a spectroscopic system capable of achieving ultrawide FOV without the need for stitching spectrograph subsystems. Additionally, it also designs a front-end telescope system that matches the spectroscopic system. The spectroscopic system features a slit length of 240 mm, employing an enhanced Offner structure for a long slit spectroscopic system, incorporating a freeform surface on the third mirror. To inhibit the effects of radiation stray light, the system's exit pupil is controlled to be positioned in front of the image plane to facilitate matching with the cold shield. The analysis indicates that the spectral resolution of the long-wave infrared imaging spectrometer system is 50 nm, with a total of 90 spectral sampling channels. The system's spatial resolution is 100 m, enabling a swath width of 400 km. Furthermore, the modulation transfer function (MTF) exceeds 0.42 at the Nyquist frequency of 8.35 lp/mm. The maximum RMS radius of the system is less than 27 μm at wavelengths ranging from 8 to 12.5 μm.

New shape optimization method for tree structures based on BP neural network

To realize the intelligent optimization for the tree structures supporting freeform surface roof or bearing uneven load, a new shape optimization method based on the back-propagation (BP) neural network is proposed. This method enables the intelligent positioning of hierarchical nodes through a recursive approach from top-down, with the aim of satisfying the zero bending moment and structural stability. Using three-dimensional tree structures as an example, this study provides a detailed description of the implementation method and steps of intelligent shape optimization, along with a comparative analysis with the reverse-hang recursive approach. Results indicate that the proposed approach effectively addresses the challenge of locating load-bearing centers in tree structures with uneven loads or freeform surface roofs. It not only demonstrates universality for tree structures under complex engineering conditions, but also enhances efficiency and intelligence in the structure optimization design.

Tailored porosity in additive manufacturing of 7075 aluminum alloy for crack suppression and high strength

Laser-directed energy deposition (LDED) additive manufacturing of 7075 aluminum (Al) alloy is highly challenging due to the inherent poor printability and high cracking tendency. Here, we disclose a new approach to suppress cracking in LDED-processed 7075 Al alloy by engineered porosity (about 1.14 %). The crack-free 7075 Al alloy was achieved by slightly sacrificing the densification. Further increasing the density of the material by increasing laser energy input leads to cracking. The mechanisms of minor pores in alleviating cracks are mainly reflected in three aspects: (i) pores disrupt the epitaxial growth of columnar grains; (ii) free-form surfaces surrounding pores could release the accumulated residual stress, and (iii) more dislocations near pore drive nucleation of near equiaxed grains. The LDED-processed crack-free 7075 Al alloy after heat treatment shows an ultimate tensile strength of 464 ± 12 MPa and break elongation of 9.7 ± 1.2 %, attaining a good strength-ductility synergy among many additively manufactured 7075 Al alloys in the current literature. Unlike the mainstream additive manufacturing of metallic materials, which pursues high densification to attain high-performance components, this work demonstrates the positive roles of pores in the additive manufacturing of cracking-sensitive materials. The findings of this work highlight new insights regarding the balance between pores and cracks for better manufacturability and higher mechanical performance of materials.

A General Approach for Constrained Robotic Coverage Path Planning on 3D Freeform Surfaces

A General Approach for Constrained Robotic Coverage Path Planning on 3D Freeform Surfaces

Viewpoint Planning of Robotic Measurement System for Free-Form Surfaces Based on Visibility Cone Space Explorer

Viewpoint Planning of Robotic Measurement System for Free-Form Surfaces Based on Visibility Cone Space Explorer

Study on robot trajectory planning and coating thickness prediction for plasma spraying on complex surface

Plasma spraying techniques are commonly employed for the deposition of thermal barrier coatings (TBCs) due to their efficiency and cost-effectiveness. However, ensuring uniform coating thickness and quality on complex free-form surfaces poses significant challenges. This paper investigates the influence of spraying trajectory and related parameters (spraying distance, angle, velocity) on coating thickness distribution, addressing the need for simplified analysis among numerous variables affecting coating quality. Different from the predominantly existing research focusing on flat or rotationally symmetric substrates, this study delves into the planning of spray trajectories for free-form surfaces, which is crucial for industries dealing with complex components, such as turbine blades. Innovative optimization approaches are employed to refine spray trajectories and improve coating consistency. Through theoretical modeling, simulation and experimental validation, the impact of spray parameters on coating thickness was demonstrated. Both the mean and disperssion coefficient errors of the coating thickness, obtained by the theoretical prediction model and the spray experiments, are lower than 10 %. The normal spray trajectory makes the coatings more evenly distributed, and the coating uniformity is at least 50 % higher than that of the codirectional spraying. This research contributes to the optimization of plasma spraying processes, particularly on irregular surfaces, thereby facilitating the development of high-performance TBCs for industrial applications.

Local slope tolerance model for optical surfaces with distortion as the evaluation criterion

Ultra-precision imaging systems support cutting-edge scientific exploration and technological innovation. The continuous development of optical freeform and aspheric surface technology offers new possibilities for high-performance optical systems but also presents significant manufacturing challenges. In this paper, we derive and discuss in detail the impact of surface manufacturing errors on the image point positions of optical systems. The analysis reveals that among the manufacturing errors, the surface slope error is the primary factor driving positional changes in image points. Based on these insights, a local slope tolerance model using distortion as the evaluation criterion is proposed. This model specifies the slope error requirements at each point on the surface, ensuring the optical system's distortion meets the acceptable threshold during manufacturing. The model’s effectiveness is validated through an off-axis three-mirror freeform optical system and a Cassegrain aspheric optical system.

Topography prediction at boundaries between sub-regions in the 5-axis milling of Plexiglas based on dimension reduction method

Sub-regional milling has become an important machining method in the production of free-form surface parts. However, due to complex tool paths, irregular surface topography can occur at the region boundaries, which in turn affects the performance of the part such as the light transmission, optical distortion and mechanical strength of non-metallic transparent material etc. It is vital for manufacturers and researchers to study the forming mechanism of topography at boundaries and then to control it to get the high quality of the machined surface. Therefore, this paper thoroughly investigates the formation of surface topography at the boundary of sub-regions in the five-axis machining process. First, the boundaries of sub-regions are classified. Simultaneously, swept surfaces of the cutting edge, taking into account the process parameters and tool path, are constructed. Then, the surface topography is calculated using an improved model based on dimension reduction theory. Furthermore, through simulation and experiments, the predicted surface topographies agree well with the measured ones. Finally, some conclusions are listed and the method in this paper can provide a reliable basis for manufacturing high-quality parts.

Correction to: The contour error evaluation based on spherically-approximated patches for free-form surface

Correction to: The contour error evaluation based on spherically-approximated patches for free-form surface

Comparative Study on the Interest in Non-Uniform Rational B-Splines Representation versus Polynomial Surface Description in a Freeform Three-Mirror Anastigmat

Novel freeform optical design methods can be classified in two categories, depending on whether they focus on the generation of a starting point or the development of new optimization tools. In this paper, we design a freeform three-mirror anastigmat (TMA) and compare different surface representations using either a differential ray tracer as a new optimization tool or a commercial ray tracer (ANSYS-ZEMAX OpticStudio). For differential ray tracing, we used FORMIDABLE (Freeform Optics Raytracer with Manufacturable Imaging Design cApaBiLitiEs), an optical design library with differential ray tracing and Non-Uniform Rational B-Splines (NURBS) optimization capabilities, available under the European Software Community License (ESCL). NURBS allow a freeform surface to be represented without needing any prior knowledge of the surface, such as the polynomial degree in polynomial descriptions. OpticStudio and other commercial optical design software are designed to optimize polynomial surfaces but are not well-suited to optimize NURBS surfaces, requiring a custom optical design library. In order to demonstrate the interest in using NURBS representation, we designed and independently optimized two freeform telescopes over different iteration cycles; with NURBS using FORMIDABLE or with XY polynomials using OpticStudio. We then compared the resulting systems using their root mean square field maps to assess the optimization quality of each surface representation. We also provided a full-system comparison, including mirror freeform departures. This study shows that NURBS can be a relevant alternative to XY polynomials for the freeform optimization of reflective three-mirror telescopes as it achieves more a uniform imaging quality in the field of view.

Design of off-axis reflective dual-channel zoom freeform optical systems

In this work, two off-axis reflective dual-channel zoom optical systems are conceived and designed. These two systems achieve good imaging quality and compact system volume by introducing freeform surfaces. Firstly, the system models of the off-axis reflective dual-channel zoom optical systems are introduced, and the first-order analysis is carried out. Then, a design method of an off-axis reflective dual-channel zoom freeform optical system is introduced, and two examples are designed using this method. In one example, the two channels have a separate primary mirror and share a secondary mirror and a third mirror. The system achieves a zoom ratio of 2 times. The two different channels of the other system have separate third mirror and share the primary mirror and the secondary mirror. The system achieves a zoom ratio of 4 times. The two systems have good imaging performance close to the diffraction limit in the visible light band. Finally, the proposed off-axis reflective dual-channel zoom freeform optical system is analyzed and discussed.

A Combined Sensor Design Applied to Large-Scale Measurement Systems.

The photoelectric sensing unit in a large-space measurement system primarily determines the measurement accuracy of the system. Aiming to resolve the problem whereby existing sensing units have difficulty accurately measuring the hidden points and free-form surfaces in large components, in this study, we designed a multi-node fusion of a combined sensor. Firstly, a multi-node fusion hidden-point measurement model and a solution model are established, and the measurement results converge after the number of nodes is simulated to be nine. Secondly, an adaptive front-end photoelectric conditioning circuit, including signal amplification, filtering, and adjustable level is designed, and the accuracy of the circuit function is verified. Then, a nonlinear least-squares calibration method is proposed by combining the constraints of the multi-position vector cones, and the internal parameters of the probe, in relation to the various detection nodes, are calibrated. Finally, a distributed system and laser tracking system are introduced to establish a fusion experimental validation platform, and the results show that the standard deviation and accuracy of the three-axis measurement of the test point of the combined sensor in the measurement area of 7000 mm × 7000 mm × 3000 mm are better than 0.026 mm and 0.24 mm, respectively, and the accuracy of the length measurement is within 0.28 mm. Further, the measurement accuracy of the hidden point of the aircraft hood and the free-form surface is better than 0.26 mm, which can meet most of the industrial measurement needs and expand the application field of large-space measurement systems.