Surface Form Error Research Articles

Planar oscillation-enabled deterministic magnetorheological micro-polishing

Micro-optics are attracting ever-increasing attention in advanced optical systems owing to their merits of high optical performance and high structure compactness. Although deterministic polishing is crucial for obtaining optically qualified components, the decreased micro-optic feature size imposes significant challenges on the polishing process. To proceed the post-processing technique for micro-optics, we developed a novel magnetorheological micro-polishing (μMRP) method, which features a non-contact and deterministic removal of the workpiece materials. An electromagnetic polishing tool for stiffening the MR slurry was specially designed to tightly focus the high-gradient magnetic field within a small region around the tip, thereby enabling the material removal to occur at the micro-scale. The pulse-width modulation (PWM) control strategy for the excitation currents could continuously refresh the MR slurry in the polishing, as well as precisely control the material removal. Moreover, a planar dual-axial oscillation was employed to move the tool to generate relative motions between the abrasives and workpieces for removing the materials. In practice, smooth Gaussian-shape footprints with full width at half-maximum (FWHM) around hundreds of micrometers were achieved, and the influence of the working gap, oscillation frequency, and duty ratio on the material removal was further investigated. Finally, the deterministic material removal capability was demonstrated by generating a sinusoidal micro-grid surface with an amplitude of 80 nm and a spatial period of 600 μm. The surface roughness and form error were about Sa = 1.027 nm and 6.5 nm (RMS), demonstrating that the developed μMRP is promising for figuring micro-optics.

Pre-tension design and research of cable net structure for space modular deployable antenna

Modular deployable antennas represent an ideal structural form for the development of large-aperture antennas because of their flexibility, adaptability, and high versatility. To enhance the surface accuracy of the antenna after deployment, a comprehensive pre-tension design method that considers truss deformation and tension uniformity is proposed. First, the configuration design of the antenna cable net is constructed, and the mathematical models for cable length under surface accuracy requirements and boundary nodes are established considering catenary effects. Second, the distribution patterns of cable net structure nodes and segments are analyzed, leading to the creation of node coordinate matrices and cable net connection matrices. A basic model for cable net pre-tension design is developed based on the fundamental principles of force density. Furthermore, a multi-objective optimization of cable net pre-tension is performed using a genetic algorithm, considering truss structure deformation and tension uniformity as dual factors. Finally, the developed model is applied to design a single-module cable net structure, and numerical simulation is used for validation. Research results show that the overall surface form error is 0.32 mm, and the maximum tension ratio of cable net on the front cable net surface is 1.54, whereas the maximum tension ratio of tension ties is 2.28, thereby meeting the design requirements. Numerical simulation shows that the maximum deformation of the cable net structure is 0.16 mm, validating the correctness of the model. This research can provide valuable insights and references for the pre-tension design and research of cable net structures in other antennas.

Chatter Stability of Orthogonal Turn-Milling Process in Frequency and Discrete-Time Domains

Abstract As the industry seeks better quality and efficiency, multitasking machine tools are becoming increasingly popular owing to their ability to create complex parts in one setup. Turn-milling, a type of multi-axis machining, combines milling and turning processes to remove material through simultaneous rotations of the cutter and workpiece with the translational feed of the tool. While turn-milling can be advantageous for large parts made of hard-to-cut materials, it also offers challenges in terms of surface form errors and process stability. Because tool eccentricity and workpiece rotation lead to more complexity in process mechanics and dynamics, traditional milling stability models cannot predict the stability of turn-milling processes. This study presents a mathematical model based on process mechanics and dynamics by incorporating the unique characteristics of the orthogonal turn-milling process to avoid self-excited chatter vibrations. A novel approach was employed to model time-varying delays considering the simultaneous rotation of the tool and workpiece. Stability analysis of the system was performed in both the discrete-time and frequency domains. The effects of eccentricity and workpiece speed on stability diagrams were demonstrated and validated through experiments. The results show that the tool eccentricity and workpiece speed alter the engagement geometry and delay in the regeneration mechanism, respectively, leading to significant stability diagram alterations. The proposed approach offers a comprehensive framework for the stability of orthogonal turn-milling and guidance for the selection of process conditions to achieve stable cuts with enhanced productivity.

Force servo nano-precision diamond cutting of freeform surfaces on a micro-precision machine

This paper presents force servo single point diamond cutting of freeform surfaces with nano-precision on a micro-precision machine. For nanometric machining accuracy, traditional diamond cutting based on position servo, requires accurate machine axial motions by ultra-precision machine with high cost, or utilizes a fast tool servo to compensate for machine slide vibration and motion error of common machines that is a complicated procedure. In this paper, nanometric machining accuracy was achieved on a micro-precision machine by force servo diamond cutting, in which the tool can be driven to trace the workpiece surface to compensate for the machine slide vibration, machine motion errors and workpiece incline errors accurately and automatically. For highly sensitive and stable force controlling, force servo nanocutting mechanism (FSNM) based on flexible structures was designed with force sensing resolution down to submillinewton level, and a damping controller was developed to suppress the resonant vibration of the FSNM. For extending application of force servo cutting from fabrication of only discontinuous microstructures to continuous freeform surfaces, referring force maps were developed by considering the real material removal volume of each cutting point. Force servo cutting was then validated by fabricating freeform surfaces with surface form errors of less than 10 nm on silicon spherical surfaces based on the micro-precision machine. The works discussed in this paper provide an effective technique for the fabrication of complex and continuous microstructured and freeform surfaces with nano-precision by common machines only with micron even tens of microns precision.

Development analysis of magnetorheological precession finishing (MRPF) technology.

Magnetorheological polishing (MRF) has emerged as a critical non-contact sub-aperture polishing technology due to its notable attributes of high precision and minimal damage. However, MRF's inherent D-shaped removal function leads to reduced convergence efficiency of surface form error and introduces mid-spatial-frequency (MSF) waviness. To address these challenges, we propose magnetorheological precession finishing (MRPF) technology, which ingeniously combines MRF with bonnet precession polishing to generate a Gaussian-like removal function. A pivotal component of what we believe to be a novel approach is the design and fabrication of a specialized hemispherical magnetorheological precession polishing head. The design process incorporates magnetostatic simulations and magnetic force analysis to determine the optimal generating conditions for magnetorheological ribbons. Spot polishing experiments confirm the suitability of a 30° precession angle. Experimental results demonstrate that 8-step polishing achieves a Gaussian-like removal function. Additionally, uniform polishing of fused quartz surfaces significantly reduces Ra from 0.7 µm to 2.14 nm. This research showcases the feasibility of MRPF as a new technical route to achieve Gaussian-like removal functions and nanometer-scaled surface roughness.

The machinability of titanium alloy thin-wall parts in cooling minimum quantity lubrication (CMQL) environments

The machining of thin-wall components made of titanium alloys is challenging because the poor machinability of the material leads to severe problems such as accelerated tool wear and poor surface quality, while the weak rigidity of the thin-wall structure results in unavoidable vibration and surface form errors. To address these issues, this paper investigated the mechanisms and performance of cooling minimum quantity lubrication (CMQL) in milling titanium thin-wall parts. To verify the efficiency of CMQL, different cooling/lubrication strategies, including conventional flood cooling, minimum quantity lubrication (MQL) and CMQL with different temperature levels, were investigated. The cutting force, tool wear state, chip formation, surface integrity, and surface form errors were compared and analysed in detail. The experiment results show that MQL is inadequate at higher spindle speeds due to its ineffective cooling capacity and weakened lubrication ability. In contrast, CMQL has demonstrated its feasibility and superiority in milling titanium thin-wall parts under all conditions. The outcomes indicate that a lower temperature level of CMQL is advantageous to producing better wear resistance and lower thermomechanical loads, and the CMQL (− 15 ºC) machining environment can remarkably improve the overall machining performance and control the surface form errors of the machined thin-wall parts. At the spindle speed of 3000 rpm, the surface roughness measured under CMQL (− 15 °C) condition is reduced by 16.53% and 23.46%, the deflection value is decreased by 54.74% and 36.99%, while the maximum thickness error is about 53.51% and 20.56% smaller in comparison to flood cooling and MQL machining. In addition, CMQL is an economical and sustainable cooling/lubrication strategy; the outcomes of this work can provide the industry with useful guidance for high-quality machining of thin-wall components.

Ultra-precision grinding of light-weighted SiC aspheric mirror

Based on the approximate 3D model of light-weighted SiC aspheric mirror, the deformation and stress at different positions along the radius caused by the grinding force on the mirror surface was analysed. Then the influence of processing parameters on grinding force was experimentally studied, and the prediction model of grinding force was established. Finally, the grinding experiment of light-weighted SiC aspheric mirror was carried out. The PV value of the aspheric surface form error was 4.15μm, and the Ra of surface roughness was about 28nm. The experimental results verified the feasibility of ultra-precision forming of lightweight SiC mirror by controlling grinding force based on process parameters.

Least-squares phase-shifting algorithm of coherence scanning interferometry with windowed B-spline fitting, resampled and subdivided phase points for 3D topography metrology

3D topography metrology of optical micro-structured surfaces is critical for characterizing surface texture and form errors. The coherence scanning interferometry (CSI) faces many challenges for improving the accuracy of 3D topography metrology. In this paper, the least-squares (L-S) phase-shifting algorithm of coherence scanning interferometry with windowed B-spline fitting, resampled and subdivided phase points is proposed, which provides high accuracy of 3D surface topography. The proposed algorithm avoids the introduction of complex judgment criterion of fringe orders, and tedious phase unwrapping. Comparison with generalized phase-shifting algorithm, the wrong textures do not appear on the reconstructed 3D surfaces and 2D profiles for optical grating and Micro-lens array (MLA) surfaces using the proposed algorithm. Experimental results show that a VLSI step surface has high repeated measurement accuracy with a standard deviation of 1.6 nm, the periodic error of the proposed algorithm for PMMA MLA sub-aperture units is about 20 nm, and the mean value of PMMA MLA four random sub-aperture units are 6.66 nm (Sq), 77.63 nm (Sp), 36.38 nm (Sv), 114.18 nm (Sz) and 4.90 nm (Sa), respectively.

IntelliScan: Improving the quality of x-ray computed tomography surface data through intelligent selection of projection angles.

X-ray computed tomography (XCT) enables the dimensional measurement and inspection of highly geometrically complex engineering components that are unmeasurable using optical and tactile instruments. Conventional XCT scans use a circular scan trajectory where X-ray projections are acquired with a uniform angular spacing; this approach treats all projections as being of equal importance, in practice, some projections contain more object information than others. In this work we capitalize on this concept by intelligently selecting projections with a view to improve the quality of surface models extracted from an XCT data-set. Our approach relies on using a priori object information to select X-ray projections in which the surfaces of the object are aligned with a ray-path, thus ensuring the surface of the object is fully sampled. Results are presented showing that the proposed method is able to reduce CAD comparison errors by 16%, reduce surface form error by 3%, and improve edge contrast by 14% for a machined aluminium component.

Absolute wavelength scanning interferometry for measuring the thickness of optical elements.

A technique for measurement of the thickness of optical elements using absolute wavelength scanning interferometry is presented in this paper. To achieve high-grade optical components and systems, the thickness of both planar and non-planar optical components must be measured with an accuracy of a few micrometers. The proposed technique is based on the Fizeau interferometer and interconnects data from three different tunable laser diodes yielding a long effective wavelength range and thus low measurement uncertainty. The uncertainty of the central thickness measurement ranges from hundreds of nanometers to a few microns. The method allows to measure the thickness of both flat optical elements as well as lenses with curved surfaces. Moreover, the areal information provided by the interferometry and its high angle sensitivity help to quickly and precisely align the measured component and reduce misalignment errors. The results of thickness measurements have been validated and cross-tested with other techniques. In addition to the thickness, the technique provides some additional information (wedge, surface form error) in the case of flat samples and can be easily and quickly modified (mounting of a Fizeau transmission sphere) to measure other essential parameters of optical elements. Thus, this one approach can replace many single-purpose measuring devices while maintaining high accuracy.

Ultra-precision manufacturing of microlens arrays using an optimum machining process chain.

There are still significant challenges in the accurate and uniform manufacturing of microlens arrays (MLAs) with advanced ultra-precision diamond cutting technologies due to increasingly stringent requirements and shape complexity. In this paper, an optimum machining process chain is proposed based on the integration of a micro-abrasive fluid jet polishing (MAFJP) process to improve the machining quality by single point diamond turning (SPDT). The MLAs were first machined and compensated by SPDT until the maximum possible surface quality was obtained. The MAFJP was used to correct the surface form error and reduce the nonuniformity for each lens. The polishing characterization was analyzed based on the computational fluid dynamics (CFD) method to enhance the polishing efficiency. To better polish the freeform surface, two-step tool path generation using a regional adaptive path and a raster and cross path was employed. Moreover, the compensation error map was also investigated by revealing the relationship between the material removal mechanism and the surface curvature and polishing parameters. A series of experiments were conducted to prove the reliability and capability of the proposed method. The results indicate that the two integrated machining processes are capable of improving the surface form accuracy with a decrease in PV value from 1.67 µm to 0.56 µm and also elimination of the nonuniform surface error for the lenses.

Measurement and correction of lateral distortion in a Fizeau interferometer based on the self-calibration technique.

The lateral distortion of a surface measuring Fizeau interferometer may cause distorted image features in the lateral direction, as well as the surface form error in the axial direction (which is a source of the retrace error). Traditional method for lateral distortion measurement requires a high-accuracy calibration plate featuring a grid pattern. Such a calibration plate is not always available, especially when the required accuracy of the grid pattern comes to the order of sub-micrometer or even nanometer level. To remove the dependence on the plate accuracy, we propose a self-calibration method for the measurement and correction of lateral distortion in Fizeau interferometer. The self-calibration technique may separate the lateral distortion and the geometric error of the calibration plate. This method is verified using a 108-mm-aperture Fizeau interferometer. The experiments show that the form measurement error of a surface tilted at approximately 5° and 16° can be reduced from 92 nm to 43 nm and from 251 nm to 144 nm (peak-to-valley value), respectively, after the distortion correction.

Matching Measurement Strategy and Form Error Compensation for Freeform Surface Machining Based on STS Turning

The freeform surface quality is limited by the measurement, and form error cannot be convergent via compensation machining. This paper proposed a surface matching measurement strategy based on the least squares principle and iterative precision adjustment to precisely obtain surface form error after manufacturing by single point diamond turning. Through the coordinate transformation of translation and rotation, the measured surface was aligned with theoretical surface at the same coordinate system. The corresponding simulation was carried out to verify the performance of the proposed method, and the simulation results indicated that this method can achieve accurate alignment in a sub-nanometer range. Finally, with XY polynomial freeform surface as the ideal surface, compensation experiments were undertaken. The form error of freeform converged continuously after compensation machining for three times, during which the form accuracy of PV and RMS were down to 335 nm and 34 nm respectively from 1.4 um and 173 nm. The results showed that capability of the proposed compensation method was verified and the form accuracy could be improved effectively.

Free-form surface form error evaluation based on smaller-scale sampling points in touch-trigger probing

Surface reconstruction is an essential operation in the evaluation of free-form surface form error. As a feasible technology in free-form surface sampling, touch-trigger probing has been widely used in on-machine measurement and coordinate measurement machine. However, surface reconstruction quality is influenced by limited sampling point size. This study proposes a surface reconstruction method based on surface position error and deformation error model. Surface form error is decomposed into surface position error and deformation error. Then, the design surface is taken as a rigid body, and a point-to-surface function-based iterative algorithm is conducted to adjust surface location and orientation to best match the sampling points. The advantage of this algorithm is that it considers the probe dimension, so further compensation of probe radius is not required. The geometry of the adjusted design surface is modified based on thin plate energy minimization and point-to-surface function. Due to the inherent feature of the proposed method, geometric features of the design surface are kept. Experiments are conducted to verify the effectiveness of the proposed method, and results show that the proposed method can achieve lower error compared with existing methods.

Effects of wheel spindle error motion on surface generation in grinding

In ultra-precision grinding, error motions of the aerostatic bearing wheel spindle lead to unexpected variations in the actual depth of cut, thereby directly affecting machining accuracy. However, few studies have focused on dynamic characteristics of the wheel spindle error motion and its effects on surface generation. In this paper, the ground surface generation mechanism under the wheel spindle error motion is explored by establishing a grinding kinematics-based surface topography model integrated with a wheel spindle dynamics model considering the wheel topography and the overlapping effect. Grinding experiments are performed to identify the theoretical results through spindle vibration signals and machined surface topographies. The results show that the spindle error motions include the drift of the axis average line which produces the surface form error, and the spindle vibration relative to the axis average line that contributes to the waviness circumferentially. It is also found that the increasing wheel speed leads to the decreasing waviness amplitude at a small radial distance of the workpiece while the trend of the waviness amplitude with the wheel speed is the same as that of the spindle vibration amplitude at a large radial distance. Furthermore, based on the ground surface simulation, the grinding mark pattern formation mechanism is found to include three types, identified by the machined surfaces. A novel and convenient method, where the ratio of the grinding contact width to the cross feed distance per workpiece revolution and the reduced fraction of rotational speed ratio are used, is proposed to predict the grinding mark patterns and spatial frequencies, and validated by the ground surface simulation and experimental results.

Extended classification of surface errors shapes in peripheral end-milling operations

The prediction of form surface error represents the basis of many approaches, which aims at increasing the productivity and reducing the costs of a milling operation. In peripheral end-milling the form error caused by the tool/workpiece static deflection is not constant along the axial depth of cut, and it presents different shapes due to the cutting forces, which change according to the cutting strategy, end-mill geometry and cutting parameters, making the surface error prediction complex and time consuming. This paper presents a comprehensive classification of the shape of the cutting forces which cause the surface form errors, in both up and down-milling. The proposed classification includes analytical equations to obtain the axial position of key points (also known as kinks) defining the surface error shape in any cutting condition and tool geometry. The results given by the developed classification were experimentally validated trough different cutting tests to prove the reliability and the effectiveness of the proposed approach. The proposed classification and formulations manage to identify the surface error shapes both when several flutes are involved in the process and aggressive axial depths of cut are adopted, extending the knowledge about surface errors in peripheral milling. Furthermore, the proposed formulations could be exploited to ease error prediction methods based on simulations or drastically reduce the surface measuring time in quality control.

A state-of-art review on chatter and geometric errors in thin-wall machining processes

Thin-wall components are some critical parts that are extensively used in modern industries due to their high structural efficiency and low specific weight. However, precision machining of flexible thin-wall components has been a challenging task accompanied by many inevitable issues such as unexpected chatter vibration and large surface form errors. To solve these inherent problems and improve the machining quality, plenty of research has been carried out in the last decades. In this paper, a comprehensive review of previous studies on thin-wall machining process and issues has been conducted; The state-of-the-art technologies recently developed are introduced, and an in-depth discussion of both chatter vibration and thin-wall deformation have been presented in terms of the theories, mechanisms, the prediction, monitoring and elimination methods. Finally, development trends are summarized, and recommendations for future works are proposed based on the extensive review and the analysis of practical problems.

Adaptive spiral tool path generation for computer numerical control machining using point cloud

This paper reports a novel method to generate adaptive spiral tool path for the CNC machining of complex sculptured surface represented in the form of cloud of points without the need for surface fitting. The algorithm initially uses uniform 2 D circular mesh-grid to compute the cutter location (CL) points by applying the tool inverse offset method (IOM). These CL points are refined adaptively till the surface form errors converge below the prescribed tolerance limits in both circumferential and radial directions. They are further refined to eliminate the redundancy in machining and generate optimum region wise tool path to minimize the tool lifts. The NC part programs generated by our algorithm were widely tested for different case studies using the commercial CNC simulator as well as by the actual machining trial. Finally, a comparative study was done between our developed system and the commercial CAM software. The results showed that our system is more efficient and robust in terms of the obtained surface quality, productivity, and memory requirement.

Pre-Compensation of Mold in Precision Glass Molding Based on Mathematical Analysis.

Precision glass molding is the most appropriate method for batch production of glass lenses with high surface accuracy and qualified optical performance. However, the form error caused by material expansion and contraction is the main factor affecting the precision of the molded lenses, thus the mold must be pre-compensated. In this paper, an effective method of mold pre-compensation based on mathematical analysis is established. Based on the thermal expansion curve of D-ZK3 glass, the freezing fictive temperature of the glass under the actual cooling rate is measured, and the mold pre-compensation factor can be quickly calculated. Experimental results show that the peak valley (PV) value of the surface form error of molded aspheric lens with an aperture of 5.3 mm is effectively reduced from 2.04 μm to 0.31 μm after the pre-compensation, thus meeting the geometric evaluation criterion.

Preparation of Flat and Smooth Copper Surface by Jet Electrochemical Machining and Electrochemical Polishing

Ultra-flat and ultra-smooth copper (Cu) surfaces are widely used as optical mirrors, heat sinks, and substrates for functional material growth. Traditional polishing methods that rely on abrasive particles are easy to induce mechanical defects such as abrasives embedding and scratches on surfaces. A new stress-free machining process is proposed in this research to fabricate an ultra-flat and ultra-smooth Cu surface by combining jet electrochemical machining (Jet-ECM) and electrochemical polishing (ECP). With the accurate manipulating of material removal rate (MRR) and planning of nozzle trajectory, an ultra-flat surface can be obtained efficiently in the Jet-ECM process. The surface roughness of the workpiece can be further improved by ECP with the same electrolyte used in the Jet-ECM process. The results show that the surface peak-to-valley (PV) value which indicated the surface form error of the Cu surface was reduced from 4.4 μm to 1.7 μm and the surface roughness Sa was reduced from 70.3 nm to 13.5 nm. The combination of Jet-ECM and ECP which share the same electrolyte and apparatus can improve the surface flatness and roughness significantly. This study improves the machining accuracy of stress-free machining methods and has great implications for the further understanding of the electrochemical removal mechanism.