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Journal articles on the topic 'Milling machinery – Calibration'
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1
Mareš, Martin, Otakar Horejš, and Jan Hornych. "Thermal Error Minimization of a Turning-Milling Center with Respect to its Multi-Functionality." International Journal of Automation Technology 14, no. 3 (May 5, 2020): 475–83. http://dx.doi.org/10.20965/ijat.2020.p0475.
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Achieving high workpiece accuracy is a long-term goal of machine tool designers. Many causes can explain workpiece inaccuracy, with thermal errors being the most dominant. Indirect compensation (using predictive models) is a promising thermal error reduction strategy that does not increase machine tool costs. A modeling approach using transfer functions (i.e., a dynamic method with a physical basis) has the potential to deal with this issue. The method does not require any intervention into the machine tool structure, uses a minimum of additional gauges, and its modeling and calculation speed are suitable for real-time applications that result in as much as 80% thermal error reduction. Compensation models for machine tool thermal errors using transfer functions have been successfully applied to various kinds of single-purpose machines (milling, turning, floor-type, etc.) and have been implemented directly into their control systems. The aim of this research is to describe modern trends in machine tool usage and focuses on the applicability of the modeling approach to describe the multi-functionality of a turning-milling center. A turning-milling center is capable of adequately handling turning, milling, and boring operations. Calibrating a reliable compensation model is a real challenge. Options for reducing modeling and calibration time, an approach to include machine tool multi-functionality in the model structure, model transferability between different machines of the same type, and model verification out of the calibration range are discussed in greater detail.
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Wang, Shih Ming, Han Jen Yu, Jih Pong Yang, and Da Fan Chen. "Development of an On-Machine Machining Error Measurement and Compensation System for Micro Milling Process." Key Engineering Materials 447-448 (September 2010): 529–33. http://dx.doi.org/10.4028/www.scientific.net/kem.447-448.529.
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To further enhance the accuracy of a micro milling process, an effective error measurement method and error compensation method are necessary. An on-machine vision-based error measurement method integrating image re-constructive technology, camera pixel correction, and model comparison algorithm to provide the capability of non-contact measurement for micro-machined workpiece error was developed. With use of Canny Edge Detection algorithm and camera pixel calibration, the edge of the contour of a machined workpiece can be identified and used to re-construct the actual shape of the workpiece. The actual shape will then be compared to the theoretical shape of the workpiece. To prove the feasibility of the proposed methods and system, experiments were conducted. The results have shown the success of enhacing machining accuracy for a micro milling process.
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Rakhmanov, S. R., Yu G. Gulyaev, and S. V. Zdanevich. "The dynamics of the centreing mechanism of piercing mill mandrel of the pipe-rolling plant." Computer Modeling: Analysis, Control, Optimization 7, no. 1 (2020): 51–63. http://dx.doi.org/10.32434/2521-6406-2020-1-7-51-63.
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The paper presents the results of the vibrodiagnostics of a centering machine mechanism for holding piercing mill mandrel N1 of the pipe-rolling plant (PRP) 350. In the paper, it is established that vibration acceleration of a bearing roller lever of the centering machine mechanism for holding piercing mill mandrel during milling of an Æ282х50 mm shell, steel 20 reaches 5…12 m/s2, and of the upper roller’s vibration frequency is 33.3 Hz. The paper presents the results of the thickness measuring of the Æ282х50 shell, steel 20 after using the piercing mill N1 350. The results shows the distinctive influence of the dynamics of the milling holding mechanism rod. The system is put forth for calculating the energy-power parameters during the realization of the technical process for making shells of the required specifications in a piercing mill. The paper establishes the value of the milling axial resistance to the flow of the milled metal (taking the calibration values into account). The paper presents a refined system for making a dynamic model for the piercing bill milling holding mechanism rod with the milling calibration parameters taken fully included. A differential equation for the milling rod movement is made, specifically for the dynamic model of the PRP piercing mill mechanical system. The dynamic values of the mechanical system are refined, which is used as a starting point for solving the tasks dealing with the analysis of the PRP piercing mill milling rod’s vibroactivity state. In order to decrease rod vibroactivity levels, the paper recommends choosing rational milling calibration and to set the shell milling modes using mechanical system dynamics modelling during the corresponding stages of the design of technological processes. The paper pro-poses a scheme for modernization of the PRP 350 piercing bill exit side by switching the centering machine rod system holding bridges gear to proportional hydraulics. Keywords: piercing mill, vibration diagnostics, thickness measurement, piercing, sleeve; difference in wall thickness, energy-power parameters, calibration, mandrel, vibroactivity, dynamics, mandrel retention mechanism.
4
Mares, M., and O. Horejs. "ENHANCEMENT OF SPECIALISED VERTICAL TURNING LATHE ACCURACY THROUGH MINIMISATION OF THERMAL ERRORS DEPENDING ON TURNING AND MILLING OPERATIONS." MM Science Journal 2021, no. 3 (June 30, 2021): 4512–18. http://dx.doi.org/10.17973/mmsj.2021_7_2021053.
Full textAbstract:
Achieving high workpiece accuracy is a long-term goal of machine tool designers. There are many causes of workpiece inaccuracy, with thermal errors being the most dominant. Indirect compensation (using predictive models) is a promising strategy for reducing thermal errors without increasing machine tool cost. A modelling approach using thermal transfer functions (a dynamic method with a physical basis) embodies the potential to deal with this issue. The method does not require interventions into the machine tool structure, uses a minimum of additional gauges and its modelling and calculation speed is suitable for real-time applications with fine results with up to 80% thermal error reduction. Advanced machine tool thermal error compensation models have been successfully applied on various kinds of single-purpose machines (milling, turning, floor-type, etc.) and implemented directly into their control systems. This research reflects modern trends in machine tool usage and as such is focused on the applicability of the modelling approach to describe specialised vertical turning lathe versatility. The specialised vertical turning lathe is adequately capable of carrying out turning and milling operations. Calibration of the reliable compensation model is a real challenge. The applicability of the approach during immediate switching between turning and milling operations is discussed in more detail.
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Iñigo, Beñat, Ander Ibabe, Gorka Aguirre, Harkaitz Urreta, and Luis Norberto López de Lacalle. "Analysis of Laser Tracker-Based Volumetric Error Mapping Strategies for Large Machine Tools." Metals 9, no. 7 (July 5, 2019): 757. http://dx.doi.org/10.3390/met9070757.
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The measurement and compensation of volumetric error in milling machines of medium and large size is a key aspect to meeting the precision requirements of the most demanding applications. There are several solutions for volumetric error measurement—usually based on laser or in calibrated artifacts—that offer different specifications and lead to a variety of levels of precision, complexity of implementation and automation, cost of equipment, and measurement time, amongst others. Therefore, it is essential to have tools that allow, in each case, analysis as to which is the optimal calibration strategy, providing the criteria for evaluating different measurement equipment and strategies. To respond to this need, several tools have been developed which are able to simulate the entire calibration and compensation process (machine, measurement, model adjustment, etc.) and apply optimization methods to find the best measurement strategy for each application. For a given machine architecture and expected error ranges, the compensation error for each strategy is obtained by propagating measurement uncertainties and expected machine errors through the measurement and compensation model fitting process by Monte Carlo simulations. The use of this tool will be demonstrated through the analysis of the influence of the main design parameters of a measurement strategy for the calibration of a 3-axis machine tool, based on the measurement of tool position with a laser tracker.
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Mancisidor, Iker, Xavier Beudaert, Gorka Aguirre, Rafael Barcena, and Jokin Munoa. "Development of an Active Damping System for Structural Chatter Suppression in Machining Centers." International Journal of Automation Technology 12, no. 5 (September 5, 2018): 642–49. http://dx.doi.org/10.20965/ijat.2018.p0642.
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The presence of chatter vibrations is one of the main limitations of machining processes in terms of productivity, as they prevent obtaining the required surface finishes and decrease the life of tools and the mechanical elements of the machine. The use of active dampers governed by a control strategy permits an increase in structural damping without significantly changing the machine design. The main objective of this study is to improve the dynamic capabilities of the machine, and to increase the chatter-free region. This objective is achieved by the addition of an electromagnetic actuator located as close as possible to the cutting point. The electromechanical design of the actuator is described, and a novel double flexure guarantees a constant gap between the moving magnets and the coils. This smart mechatronic system allows the introduction of new additional functions: process and machine monitoring, chatter avoidance by spindle speed modification, and machine dynamics calibration. All of these functions enhance standard milling machines.
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Subagio, Dalmasius Ganjar, Ridwan Arief Subekti, Hendri Maja Saputra, Ahmad Rajani, and Kadek Heri Sanjaya. "Three axis deviation analysis of CNC milling machine." Journal of Mechatronics, Electrical Power, and Vehicular Technology 10, no. 2 (December 18, 2019): 93. http://dx.doi.org/10.14203/j.mev.2019.v10.93-101.
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The manufacturing technology has developed rapidly, especially those intended to improve the precision. Consequently, increasing precision requires greater technical capabilities in the field of measurement. A prototype of a 3-axis CNC milling machine has been designed and developed in the Research Centre for Electrical Power and Mechatronics, Indonesian Institute of Sciences (RCEPM-LIPI). The CNC milling machine is driven by a 0.4 kW servo motor with a spindle rotation of 12,000 rpm. This study aims to measure the precision of the CNC milling machine by carrying out the measurement process. It is expected that the CNC milling machine will be able toperform in an optimum precision during the manufacturing process. Accuracy level testing is done by measuring the deviations on the three axes namely X-axis, Y-axis, and Z-axis, as well as the flatness using a dial indicator and parallel plates. The measurement results show the deviation on the X-axis by 0.033 mm, the Y-axis by 0.102 mm, the Z-axis by 0.063 mm, and the flatness of the table by 0.096 mm, respectively. It is confirmed that the deviation value is within the tolerance standard limits set by ISO 2768 standard. However, the calibration is required for this CNC milling machine to achieve more accurate precision. Furthermore, the design improvement of CNC milling machine and the application of information technology in accordance with Industry 4.0 concept will enhance the precision and realibility.
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Lian, Meng, Hai Bo Liu, Yong Qing Wang, Yang Li, Xian Jun Sheng, and Ying Wei Ying. "A Surface Normal On-Machine Measuring Method Using Eddy-Current (EC) Sensor Array." International Journal of Automation Technology 10, no. 6 (November 4, 2016): 977–84. http://dx.doi.org/10.20965/ijat.2016.p0977.
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Normal vector measurements of the machining point and attitude adjustments of the end effector are key aspects to meet the technological requirements of hole verticality in auto-drilling and the residual wall thickness in mirror milling. In this paper, a surface normal on-machine measuring method using an EC sensor array is proposed. The influences of the object surface inclination and the sensor array arrangement on the performance of EC displacement sensors were investigated, and the sensor measuring errors from coupling interference were effectively eliminated. Moreover, a practical calibration algorithm was established in which the positions of the EC sensors in a normal vector calculation model were accurately corrected. The feasibility of the measuring method was validated through a calibration experiment, as well as a measurement experiment based on the calibration results. The accuracy of a normal vector measurement is improved when applying the accuracy compensation and position calibration algorithm of an EC array to engineering practices.
9
Wang, Li-Ping, Fu-Gui Xie, Xin-Jun Liu, and Jinsong Wang. "Kinematic calibration of the 3-DOF parallel module of a 5-axis hybrid milling machine." Robotica 29, no. 4 (August 12, 2010): 535–46. http://dx.doi.org/10.1017/s0263574710000433.
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SUMMARYThis paper investigates the kinematic calibration of a 3-DOF parallel mechanism based on the minimal linear combinations of error parameters. The error mapping function between the geometric errors and the output errors is formulated and the identification matrix is generated and simplified. In order to identify the combinations of error parameters, four theorems to analyze the columns of the simplified identification matrix are introduced. Then, an anti-disturbance index is presented to evaluate the identification performance. On the basis of this index, measurement strategy is developed and optimal measuring configurations are given. After external calibration, linear interpolation compensation is applied to improve the terminal accuracy further. Results of experiment show that the method used in this paper is effective and efficient, and the errors are convergent within two iterations generally. This method can be extended to other parallel mechanisms with weakly nonlinear kinematics.
10
Pavlovčič, Urban, Peter Arko, and Matija Jezeršek. "Simultaneous Hand–Eye and Intrinsic Calibration of a Laser Profilometer Mounted on a Robot Arm." Sensors 21, no. 4 (February 3, 2021): 1037. http://dx.doi.org/10.3390/s21041037.
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A method for simultaneous laser profilometer and hand–eye calibration in relation to an industrial robot as well as its implementation is presented. In contrast to other methods, the new calibration procedure requires the measurement of only one reference geometry to calculate all the transformation parameters. The reference geometry is measured with a laser profilometer from 15 different poses. The intrinsic parameters of the profilometer, as well as the extrinsic (hand–eye) parameters, are then numerically optimized to achieve the minimum deviation between the reference and the measured geometry. The method was characterized with experiments that revealed a standard deviation of the displacements between the reference geometry after the calibration of less than 0.105 mm in the case of using the robot-arm actuator and 0.046 mm in case of using a 5-axis CNC milling machine. The entire procedure, including measurement and calculation, can be completely automated and lasts less than 10 min. This opens up possibilities for regular on-site recalibration of the entire system.
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Yablonev, Alexander, and Anna Guseva. "Method of Expanding Measurement Limits of Digital Dynamometer in Testing Strength of Moulded Peat Products." E3S Web of Conferences 174 (2020): 01035. http://dx.doi.org/10.1051/e3sconf/202017401035.
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The work is carried out to survey operating quality of sod peat produced by milling-forming machines in the field. The surveillance will help make necessary changes in mining machine designs and operating modes in a timely manner. One of the most important quality parameters of sod peat is its bending strength. To evaluate it, Tver State Technical University has developed a destruction test bench. The test bench is equipped with a digital dynamometer and a strain-gauge bracket torecord the destructive load. However, the instruments are designed for 1 kN maximum load. The bending tests of moulded peat products conducted by the authors showed that the destructive load often exceeds 1 kN, which meant that the generation and measurement limits of destructive load have to be expanded within the range of equipment being available. The problem has been solved by installing additional elements in the strain- gauge bracket and making a calibration chart. The method can expand the generation and measurement limits of destructive load by more than 50 %.
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Chun, Matthew, Robert Clarke, Benjamin J. Cairns, David Clifton, Derrick Bennett, Yiping Chen, Yu Guo, et al. "Stroke risk prediction using machine learning: a prospective cohort study of 0.5 million Chinese adults." Journal of the American Medical Informatics Association 28, no. 8 (May 9, 2021): 1719–27. http://dx.doi.org/10.1093/jamia/ocab068.
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Abstract Objective To compare Cox models, machine learning (ML), and ensemble models combining both approaches, for prediction of stroke risk in a prospective study of Chinese adults. Materials and Methods We evaluated models for stroke risk at varying intervals of follow-up (<9 years, 0–3 years, 3–6 years, 6–9 years) in 503 842 adults without prior history of stroke recruited from 10 areas in China in 2004–2008. Inputs included sociodemographic factors, diet, medical history, physical activity, and physical measurements. We compared discrimination and calibration of Cox regression, logistic regression, support vector machines, random survival forests, gradient boosted trees (GBT), and multilayer perceptrons, benchmarking performance against the 2017 Framingham Stroke Risk Profile. We then developed an ensemble approach to identify individuals at high risk of stroke (>10% predicted 9-yr stroke risk) by selectively applying either a GBT or Cox model based on individual-level characteristics. Results For 9-yr stroke risk prediction, GBT provided the best discrimination (AUROC: 0.833 in men, 0.836 in women) and calibration, with consistent results in each interval of follow-up. The ensemble approach yielded incrementally higher accuracy (men: 76%, women: 80%), specificity (men: 76%, women: 81%), and positive predictive value (men: 26%, women: 24%) compared to any of the single-model approaches. Discussion and Conclusion Among several approaches, an ensemble model combining both GBT and Cox models achieved the best performance for identifying individuals at high risk of stroke in a contemporary study of Chinese adults. The results highlight the potential value of expanding the use of ML in clinical practice.
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Nobre, Joao P., J. H. Stiffel, W. Van Paepegem, Andreas Nau, António Castanhola Batista, Maria José Marques, and Berthold Scholtes. "Quantifying the Drilling Effect during the Application of Incremental Hole-Drilling Technique in Laminate Composites." Materials Science Forum 681 (March 2011): 510–15. http://dx.doi.org/10.4028/www.scientific.net/msf.681.510.
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In this work, a methodology to quantify the effect of the drilling operation, during the application of the incremental hole-drilling technique (IHD) for measuring residual stresses in laminate composites, in particular, the polymer matrix composites (PMC), is presented. This technique will allow the optimization of the drilling procedures and its parameters, enabling the quantification of the drilling effect. This quantification is obtained by using an experimental calibration procedure followed by a numerical simulation of the whole process. The direct comparison of the experimental and numerical results will allow quantifying the effect of the drilling operation. As example, the methodology was applied to the case of carbon/epoxy cross-ply laminate [0°/90°]5s. The holes have been made by using two different drilling procedures, but the same tool geometry. High speed milling powered by air compression, a process usually employed in the case of the application of hole-drilling technique to metal alloys and a conventional computer numerically controlled (CNC) milling machine, were used. The results seem to show that incremental hole-drilling could be a reliable technique to determine residual stresses in fibre-reinforced polymers.
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Vergeest, Joris S. M., Johan J. Broek, and A. Van Voorden. "Body Surface Measurement and Replication by Photogrammetry and Computer Aided Design." Engineering in Medicine 16, no. 1 (January 1987): 3–8. http://dx.doi.org/10.1243/emed_jour_1987_016_004_02.
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This article presents and demonstrates a method of measuring the shape of the human skin and of reproducing the form as a real three-dimensional object at any scale. The working system consists of two parts, each normally in use for different disciplines at Delft University of Technology. The two parts, that we have interfaced, are a photogrammetric stereo restitution system and a CAD system integrated with a numerically controlled 3D milling machine. One stereopicture of (an arbitrary part of) the human body is sufficient to obtain any number of digitized points of the visible surface. Our system does not necessarily rely on reference grids, calibration frames, or surface marking points. Repeated measurements have shown that a measurement precision of 0.06 per cent of the observation distance is achieved. The data allow a complete surface representation by the CAD system, which in turn provides facilities for fast interactive viewing, for high quality colour image generation, and reproduction of the shape in foam material.
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Park, Seong-Hyun, Jongbeom Kim, Dong-Gi Song, Sungho Choi, and Kyung-Young Jhang. "Measurement of Absolute Acoustic Nonlinearity Parameter Using Laser-Ultrasonic Detection." Applied Sciences 11, no. 9 (May 3, 2021): 4175. http://dx.doi.org/10.3390/app11094175.
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The absolute acoustic nonlinearity parameter β is defined by the displacement amplitudes of the fundamental and second-order harmonic frequency components of the ultrasonic wave propagating through the material. As β is a sensitive index for the micro-damage interior of industrial components at early stages, its measurement methods have been actively investigated. This study proposes a laser-ultrasonic detection method to measure β. This method provides (1) the β measurement in a noncontact and nondestructive manner, (2) inspection ability of different materials without complex calibration owing to direct ultrasonic displacement detection, and (3) applicability for the general milling machined surfaces of components owing to the use of a laser interferometer based on two-wave mixing in the photorefractive crystal. The performance of the proposed method is validated using copper and 6061 aluminum alloy specimens with sub-micrometer surface roughness. The experimental results demonstrated that the β values measured by the proposed method for the two specimens were consistent with those obtained by the conventional piezoelectric detection method and the range of previously published values.
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Izamshah R.A., R., John Mo, and Song Lin Ding. "Finite Element Analysis of Machining Thin-Wall Parts." Key Engineering Materials 458 (December 2010): 283–88. http://dx.doi.org/10.4028/www.scientific.net/kem.458.283.
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In an attempt to decrease weight, new commercial and military aircraft are designs with unitised monolithic metal structural components which contains of thinner ribs (i.e., walls) and webs (i.e., floors). Most of the unitised monolithic metal structural components are machined from solid plate or forgings with the start-to-finish weight ratio of 20:1. The resulting thin-walled structure often suffers a deformation which causes a dimensional surface error due to the action of the cutting force generated during the machining process. To alleviate the resulting surface errors, current practices rely on machining through repetitive feeding several times and manual calibration which resulting in long cycle times, low productivity and high operating cost. A finite element analysis (FEA) machining model is developed in this project to specifically predict the distortion or deflection of the part during end milling process. The model aims to provide an input for downstream decision making on error compensation strategy when machining a thin-wall unitised monolithic metal structural components. A set of machining tests have been done in order to validate the accuracy of the model and the results between simulation and experiment are found in a good agreement.
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Abdulshahed, Ali M., Andrew P. Longstaff, and Simon Fletcher. "A cuckoo search optimisation-based Grey prediction model for thermal error compensation on CNC machine tools." Grey Systems: Theory and Application 7, no. 2 (August 7, 2017): 146–55. http://dx.doi.org/10.1108/gs-08-2016-0021.
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Purpose The purpose of this paper is to produce an intelligent technique for modelling machine tool errors caused by the thermal distortion of Computer Numerical Control (CNC) machine tools. A new metaheuristic method, the cuckoo search (CS) algorithm, based on the life of a bird family is proposed to optimize the GMC(1, N) coefficients. It is then used to predict thermal error on a small vertical milling centre based on selected sensors. Design/methodology/approach A Grey model with convolution integral GMC(1, N) is used to design a thermal prediction model. To enhance the accuracy of the proposed model, the generation coefficients of GMC(1, N) are optimized using a new metaheuristic method, called the CS algorithm. Findings The results demonstrate good agreement between the experimental and predicted thermal error. It can therefore be concluded that it is possible to optimize a Grey model using the CS algorithm, which can be used to predict the thermal error of a CNC machine tool. Originality/value An attempt has been made for the first time to apply CS algorithm for calibrating the GMC(1, N) model. The proposed CS-based Grey model has been validated and compared with particle swarm optimization (PSO) based Grey model. Simulations and comparison show that the CS algorithm outperforms PSO and can act as an alternative optmization algorithm for Grey models that can be used for thermal error compensation.
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Samuel, Johnson, Martin B. G. Jun, O. Burak Ozdoganlar, Andrew Honegger, Mike Vogler, and Shiv G. Kapoor. "Micro/Meso-Scale Mechanical Machining 2020: A Two-Decade State-of-the-Field Review." Journal of Manufacturing Science and Engineering 142, no. 11 (September 8, 2020). http://dx.doi.org/10.1115/1.4047621.
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Abstract Micro/meso-scale mechanical machining (M4) processes are miniaturized versions of conventional machining processes such as milling, drilling, and turning, where material removal is accomplished by physical contact between the micro/meso-scale cutting tool and the workpiece. The objective of this review paper is to provide an assessment of the state-of-the-field related to M4 processes during the last two decades. Key systems-level issues related to the deployment of M4 processes including micro/meso-scale machine tool (mMT) design, sensing/calibration, cutting tools, and lubrication strategies are discussed. Emerging material systems are identified along with the specific challenges posed for the development of microstructure-based process models. The topic of micro/meso-scale machining dynamics is reviewed both in terms of recent research findings as well as unresolved challenges posed by the complexity of experimental characterization and modeling. Finally, key industry trends are discussed along with promising interdisciplinary drivers that are expected to influence this field in the upcoming decade.
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Duan, Xianyin, Fangyu Peng, Rong Yan, Zerun Zhu, Kai Huang, and Bin Li. "Estimation of Cutter Deflection Based on Study of Cutting Force and Static Flexibility." Journal of Manufacturing Science and Engineering 138, no. 4 (October 27, 2015). http://dx.doi.org/10.1115/1.4031678.
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In the tool orientation planning for five-axis sculptured surface machining, the geometrical constraints are usually considered. Actually, the effect of nongeometrical constraints on tool orientation planning is also important. This paper studied one nongeometrical constraint which was cutting force induced static deflection under different tool orientations, and proposed a cutter deflection model based on that. In the study of the cutting force, the undeformed chip thickness in filleted end milling was modeled by geometrical analysis and coordinate transformation of points at the cutting edge. In study of static flexibility of multi-axis machine, static flexibility of the entire machining system was taken into consideration. The multi-axis machining system was divided into the transmission axes-handle (AH) end and the cutting tool end. The equivalent shank method was developed to calculate the static flexibility of the AH end. In this method, static flexibility anisotropy of the AH end was considered, and the equivalent lengths of the AH end were obtained from calibration experiments. In cutter deflection modeling, force manipulability ellipsoid (FME) was applied to analyze the static flexibility of the AH end in arbitrary directions. Based on the synthetic static flexibility and average cutting force, cutter deflections were derived and estimated through developing program realization. The predicted results were compared with the experimental data obtained by machining 300 M steel curved surface workpiece, and a good agreement was shown, which indicated the effectiveness of the cutter deflection model. Additional experiments of machining flat workpiece were performed, and the relationship of cutter deflections and tool orientations were revealed directly. This work could be further employed to optimize tool orientations for suppressing the surface errors due to cutter deflections and achieving higher machining accuracy.