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Coordinate measuring machines (CMMs) are utilized to acquire coordinate data from manufactured surfaces for inspection reasons. These data are employed to gauge the geometric form errors associated with the surface. An optimization procedure of fitting a substitute surface to the measured points is applied to assess the form error. Since the traditional least-squares approach is susceptible to overestimation, it leads to unreasonable rejections. This paper implements a modified differential evolution (DE) algorithm to estimate the minimum zone femoral head sphericity. In this algorithm, opposition-based learning is considered for population initialization, and an adaptive scheme is enacted for scaling factor and crossover probability. The coefficients of the correlation factor and the uncertainty propagation are also measured so that the result's uncertainty can be determined. Undoubtedly, the credibility and plausibility of inspection outcomes are strengthened by evaluating measurement uncertainty. Several data sets are used to corroborate the outcome of the DE algorithm. CMM validation shows that the modified DE algorithm can measure sphericity with high precision and consistency. This algorithm allows for an adequate initial solution and adaptability to address a wide range of industrial problems. It ensures a proper balance between exploitation and exploration capabilities. Thus, the suggested methodology, based on the computational results, is feasible for the online deployment of the sphericity evaluation. The adopted DE strategy is simple to use, has few controlling variables, and is computationally less expensive. It guarantees a robust solution and can be used to compute different form errors. [ABSTRACT FROM AUTHOR]

Precision glass molding (PGM) is an effective approach to manufacturing infrared chalcogenide glass (ChG) aspherical lens with complex shapes. However, infrared ChG aspherical lens often experiences form error in the designed profile and the final profile obtained by PGM. To reduce the form error of infrared ChG aspherical lens in the PGM process, a form error compensation model based on the random forest (RF) algorithm is proposed. The infrared ChG aspherical lens profile was first machined on an electroless nickel-phosphorus (Ni–P) plating to serve as the mold for PGM. After molding, the profile data of the lens was extracted, and a compensation model based on RF was constructed to optimize the model parameters using the evaluation parameters such as root mean square error (RMSE), coefficient of determination (R2), and out-of-bag (OOB). Finally, the generated compensated profile based on the compensation model was used for the compensation machining of the mold. Through this compensation approach, we have demonstrated a substantial 63.5 % reduction in the form error of the fabricated infrared ChG aspherical lens, decreasing the Peak-to-Valley (PV) value from 1.04 μm to 0.38 μm. • We propose a novel aspherical mold compensation method based on the random forest algorithm, which is applied to precision molding of Infrared Chalcogenide Glass. • Aspherical mold machining is performed on the electroless nickel-phosphorus (Ni–P) surface for precision molding, and the profile data of lens are extracted for construct the mold compensation machining model. • Through this compensation approach, we have demonstrated a substantial 63.5 % reduction in the form error of the fabricated infrared Chalcogenide Glass aspherical lens, decreasing the Peak-to-Valley (PV) value from 1.04 μm to 0.38 μm. [ABSTRACT FROM AUTHOR]

In order to investigated the main influencing factors of the error averaging ability of the orifice-compensated air bearing, an error motion prediction model of a single air pad was established, and the defined averaging coefficient was used to discuss the quantitative relationship among the error motion of the air pad,the form error of the rail and the structural parameters of the air pad. The results show that, for the long waves of the rail form error (with wave number from 0 to 1), when the wave number gradually increases, the averaging coefficient gradually decreases from 1 to close to O. For the short waves of the rail form error (with wave number from 1 to 10), when the wave number is close to or equal to a positive integer, the average coefficient takes the minimum value close to 0. And when the wave number is close to or equal to a positive integer plus 0.5, the average coefficient takes the local maximum value less than 0.25. Among the structural parameters,the width of the air land has a great influence on the error averaging ability,while the air pad gap and the diameter of the orifice restrictor basically have no influence on the error averaging ability. When the moving speed is less than 10 000 mm/s, the moving speed has a very weak influence on the error averaging ability. [ABSTRACT FROM AUTHOR]

As one of key enabling technologies in digital twin-based assembly precision analysis, three dimensional (3D) assembly tolerance analysis technology has increasingly become an important means for predicting the assembly accuracy and verifying the assembly quality of mechanical assemblies. However, current methods exist some deficiencies that (i) the traditional model mostly cannot cover geometric tolerances or form errors in 3D assembly tolerance analysis, and (ii) a loss of assembly accuracy can be caused by ignoring these parallel connections in the assembly deviation propagation. To address these issues, this study proposes a novel assembly tolerance analysis method considering form errors and partial parallel connections with assembly accuracy and reliability guarantees in mechanical assemblies. First of all, through the integration of the unified Jacobian-Torsor model and skin model shapes, the resulting integrated Jacobian-skin model shapes model is presented, which contains the two advantages of easy-to-use tolerance propagation and geometric tolerance representation. Secondly, a novel improved approach combined with progressive contact method and algebraic operation is introduced into the assembly deviation propagation, which can realize the calculation of assembly relative positioning errors in both serial and partial parallel connections. Meanwhile, an overall calculation scheme of the proposed method is elaborated for assembly tolerance analysis with a statistical way, which is used to obtain the final deviation results of the assembly functional requirements (AFRs). At last, a typical mechanical assembly involving three parts is used as a case study to illustrate the effectiveness and feasibility of this solution. [ABSTRACT FROM AUTHOR]

During milling operations, regenerative and periodic forces are generated from the interactions of cutting tools and workpieces. While the regenerative forces can be preempted by proper choice of process parameters, the periodic forces cannot. The latter induce forced responses which leave behind imprints on machined parts causing, for example, tolerance concerns. Fortunately, the responses and thus the imprints can be mitigated by proper choice of parameters. In the published literature, the imprints seem to be predominantly named according to the type of analytical treatment of the problem. They are mostly called (surface) form error (SFE) when deemed to result from static deflections at instants of periodic forces while they are mostly called surface location error (SLE) when deemed to result from dynamic responses to the periodic forces. Both SFE and SLE are referred to as periodic force induced surface error (PFISE) here. This work presents a comprehensive literature review of the available PFISE modeling methods, including concise generic explanations of the analytical formulations and the solution algorithms. The review contains more than 340 literature references which also cover data-driven methods for which measurements/images of machined surface are used to generate point cloud of surface topography from which patterns of PFISE can be identified or empirical/black box models of surface errors (which include PFISE) can be calibrated. The results of PFISE modeling is usually applied in error compensation algorithms and, hence, works on such applications are also reviewed. This literature review unveils the trends of over 6 decades and still continuing research and recommends avenues to further the research in the future. [ABSTRACT FROM AUTHOR]

Coordinate measuring machines (CMMs) are utilized to acquire coordinate data from manufactured surfaces for inspection reasons. These data are employed to gauge the geometric form errors associated with the surface. An optimization procedure of fitting a substitute surface to the measured points is applied to assess the form error. Since the traditional least-squares approach is susceptible to overestimation, it leads to unreasonable rejections. This paper implements a modified differential evolution (DE) algorithm to estimate the minimum zone femoral head sphericity. In this algorithm, opposition-based learning is considered for population initialization, and an adaptive scheme is enacted for scaling factor and crossover probability. The coefficients of the correlation factor and the uncertainty propagation are also measured so that the result’s uncertainty can be determined. Undoubtedly, the credibility and plausibility of inspection outcomes are strengthened by evaluating measurement uncertainty. Several data sets are used to corroborate the outcome of the DE algorithm. CMM validation shows that the modified DE algorithm can measure sphericity with high precision and consistency. This algorithm allows for an adequate initial solution and adaptability to address a wide range of industrial problems. It ensures a proper balance between exploitation and exploration capabilities. Thus, the suggested methodology, based on the computational results, is feasible for the online deployment of the sphericity evaluation. The adopted DE strategy is simple to use, has few controlling variables, and is computationally less expensive. It guarantees a robust solution and can be used to compute different form errors.

In ultra-precision machining (UPM), position-independent geometric errors (PIGEs), i.e., squareness errors, have a crucial impact upon the form accuracy of a machined surface. Accordingly, more research work has been conducted in PIGE identification, to improve the form accuracy. However, the general identification methods were developed without consideration of the specific squareness errors for crucial PIGEs under the form errors of the machining process. Therefore, a new method with featured structures was proposed, to identify crucial PIGEs in UPM. Firstly, a volumetric error model was developed for PIGEs, to discuss the relationship between squareness errors and their resulting machining form errors. Secondly, following the developed model, some featured structures have been proposed with their machining form errors, to significantly indicate crucial PIGEs. Finally, a series of UPM and measuring experiments were conducted for the featured structures, and then their machining form errors were measured and extracted with specific squareness errors for the identification of crucial PIGEs. The theoretical and experimental results revealed that the proposed method is simple and efficient with the featured structures to accurately identify crucial PIGEs in UPM. Significantly, the study offers a deep insight into high-quality fabrication in UPM. [ABSTRACT FROM AUTHOR]

Evaluation of the deviation zone based on discrete measured points is crucial for quality control in manufacturing and metrology. However, deviation-zone evaluation is a highly nonlinear problem that is difficult to solve using traditional numerical optimization methods. Swarm intelligence has many advantages in solving this problem: it produces gradient-free, high-quality solutions and is characterized by its ease of implementation. Therefore, this study applies an improved Harris hawks algorithm (HHO) to tackle the problem. The average fitness is applied to replace the random operator in the exploration phase to solve the problem of conflicting exploration strategies due to randomness. In addition, the salp swarm algorithm (SSA) with a nonlinear inertia weight is embedded into the HHO, such that the superior explorative ability of SSA can fill the gap in the exploration of HHO. Finally, the optimal solution is greedily selected between SSA-based individuals and HHO-based individuals. The effectiveness of the proposed improved HHO optimizer is checked through a comparison with other swarm intelligence methods in typical benchmark problems. Moreover, the experimental results of form deviation-zone evaluation on primitive geometries show that the improved method can accurately solve various form deviations, providing an effective general solution for primitive geometries in the manufacturing and metrology fields. [ABSTRACT FROM AUTHOR]

Abstract Precision grinding is a key process for realizing the use of large-aperture aspherical optical elements in laser nuclear fusion devices, large-aperture astronomical telescopes, and high-resolution space cameras. In this study, the arc envelope grinding process of large-aperture aspherical optics is investigated using a CM1500 precision grinding machine with a maximum machinable diameter of Φ1500 mm. The form error of the aspherical workpiece induced by wheel setting errors is analytically modeled for both parallel and cross grinding. Results show that the form error is more sensitive to the wheel setting error along the feed direction than that along the lateral direction. It is a bilinear function of the feed-direction wheel setting error and the distance to the optical axis. Based on the error function above, a method to determine the wheel setting error is proposed. Subsequently, grinding tests are performed with the wheels aligned accurately. Using a newly proposed partial error compensation method with an appropriate compensation factor, a form error of 3.4 μm peak-to-valley (PV) for a Φ400 mm elliptical K9 glass surface is achieved.

Micro-lens array (MLA) has been widely used for 3D imaging, etc., due to its excellent functional performances. Ultra-precision diamond turning (UPDT) offers a satisfying solution to the high-quality fabrication of MLA with sub-micrometric form accuracy and nanometric surface roughness. However, in UPDT tool setting, errors would deteriorate form accuracy as a crucial factor. This study focuses on discussing the tool setting effect on form error of MLA and proposes a new two-step tool setting method for UPDT. Firstly, a theoretical model was established for form error of MLA under tool setting errors. Moreover, a new two-step tool setting method was developed with high accuracy to control the tool setting errors. Finally, a series of experiments were carried out with different tool setting errors for the MLA fabrication, and its form error would be measured. The theoretical and experimental results are found that the proposed tool setting method is effective with a high-precision accuracy and the tool setting errors would crucially induce periodical form error at the MLA of UPDT. Significantly, the study draws up a comprehensive understanding of the tool setting effect on form accuracy of MLA in UPDT with the further improvement. [ABSTRACT FROM AUTHOR]

X-ray computed tomography (XCT) provides a unique set of dimensional measurement capabilities suitable for assessing complex geometry. However, due to the origins of XCT as a medical imaging method and qualitative non-destructive examination technique, only recently has XCT been rigorously investigated as a dimensional metrology tool. Although the data produced via XCT may be leveraged with conventional coordinate metrology techniques, the instrument physics and volumetric reconstruction methods which govern the accuracy and precision of the data are complex, workpiece-specific, and non-negligible. In particular, there is minimal prior work which has studied complex multi-step metrology tasks such as datum reference frame (DRF) construction and feature position measurement. In this work, a qualified artifact was used to evaluate the fitness of XCT for such a task. Multiple XCT systems were used, and multiple instrument magnification levels compared. The form error of planar and cylindrical features was evaluated. Further, the influence of individual feature reconstruction on the development of datums and upstream position measurements was studied. It was found that negative, i.e., bore-like, and positive, i.e., pin-like configurations of certain features were subject to distinct XCT artifact effects which caused upstream measurement errors when these features were used to construct a DRF. High magnification and X-ray scatter produced high spatial frequency noise in surface reconstruction while beam hardening and beam penetration distance variation produced gross apparent form error. The latter was associated with greater measurement errors in feature position measurement within an DRF. • A qualified artifact was dimensionally inspected using XCT. • The position of an artifact feature within a datum reference frame was assessed. • Measurement errors were attributed to apparent feature form error in datum features. • Scanning artifacts caused by beam penetration distance variation limited accuracy. • Utilizing XCT for verification tasks as per GPS/GD&T requires expert implementation. [ABSTRACT FROM AUTHOR]

The article presents a literature review dealing with the effect of the honing parameters on the quality of the machined parts, as well as with the recent innovations in honing processes. First, an overview about the honing and the plateau-honing processes is presented, considering the main parameters that can be varied during machining. Then, the influence of the honing parameters on surface finish, shape deviation and material removal rate is presented. Finally, some special and innovative applications of the honing process are described. For example, honing with variable kinematics allows obtaining oil grooves that are not rectilinear but curvilinear, in order to reduce the temperature of the part during machining and thus achieving better surface finish and lower shape deviation. Automation of the honing machines is useful to improve both the production and the verification process. Another innovation consists of using 3D printed tools in honing processes, which will help to obtain abrasive tools with complex shapes, for example by means of powder bed fusion processes. [ABSTRACT FROM AUTHOR]

In the present paper the comparison of dimensional accuracy and form errors of FFF (Fused Filament Fabrication) 3D printed spur gears obtained in two different polymeric materials (PLA and Nylon-PA6) is presented. Two types of gears were designed and printed, having different module and teeth number. First, the gear modelling process is presented. The printing parameters were defined for both materials. Then, the measuring processes were described. Using the method of the sector span, the base circular thickness and the base pitch of the gears were determined. Additionally, the root and tip diameters were measured, and their roundness and concentricity errors were determined. The analysis of the results shows that, in general, PLA allows obtaining better dimensional accuracy than Nylon. Nylon parts, which were obtained with lower infill ratio than PLA parts showed lower from errors.

In ultra-precision machining (UPM), position-independent geometric errors (PIGEs), i.e., squareness errors, have a crucial impact upon the form accuracy of a machined surface. Accordingly, more research work has been conducted in PIGE identification, to improve the form accuracy. However, the general identification methods were developed without consideration of the specific squareness errors for crucial PIGEs under the form errors of the machining process. Therefore, a new method with featured structures was proposed, to identify crucial PIGEs in UPM. Firstly, a volumetric error model was developed for PIGEs, to discuss the relationship between squareness errors and their resulting machining form errors. Secondly, following the developed model, some featured structures have been proposed with their machining form errors, to significantly indicate crucial PIGEs. Finally, a series of UPM and measuring experiments were conducted for the featured structures, and then their machining form errors were measured and extracted with specific squareness errors for the identification of crucial PIGEs. The theoretical and experimental results revealed that the proposed method is simple and efficient with the featured structures to accurately identify crucial PIGEs in UPM. Significantly, the study offers a deep insight into high-quality fabrication in UPM.

Precision grinding is a key process for realizing the use of large-aperture aspherical optical elements in laser nuclear fusion devices, large-aperture astronomical telescopes, and high-resolution space cameras. In this study, the arc envelope grinding process of large-aperture aspherical optics is investigated using a CM1500 precision grinding machine with a maximum machinable diameter of Φ1500 mm. The form error of the aspherical workpiece induced by wheel setting errors is analytically modeled for both parallel and cross grinding. Results show that the form error is more sensitive to the wheel setting error along the feed direction than that along the lateral direction. It is a bilinear function of the feed-direction wheel setting error and the distance to the optical axis. Based on the error function above, a method to determine the wheel setting error is proposed. Subsequently, grinding tests are performed with the wheels aligned accurately. Using a newly proposed partial error compensation method with an appropriate compensation factor, a form error of 3.4 μm peak-to-valley (PV) for a Φ400 mm elliptical K9 glass surface is achieved. [ABSTRACT FROM AUTHOR]

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. • Surface location error and deformation error are defined and computed to evaluate the form error. • Geometry of the measured surface is modified based on thin plate energy minimization and point-to-surface function. • Experiment results show that the reconstruction accuracy is improved by 37.9%, compared with an existing method. [ABSTRACT FROM AUTHOR]

Evaluation of the deviation zone based on discrete measured points is crucial for quality control in manufacturing and metrology. However, deviation-zone evaluation is a highly nonlinear problem that is difficult to solve using traditional numerical optimization methods. Swarm intelligence has many advantages in solving this problem: it produces gradient-free, high-quality solutions and is characterized by its ease of implementation. Therefore, this study applies an improved Harris hawks algorithm (HHO) to tackle the problem. The average fitness is applied to replace the random operator in the exploration phase to solve the problem of conflicting exploration strategies due to randomness. In addition, the salp swarm algorithm (SSA) with a nonlinear inertia weight is embedded into the HHO, such that the superior explorative ability of SSA can fill the gap in the exploration of HHO. Finally, the optimal solution is greedily selected between SSA-based individuals and HHO-based individuals. The effectiveness of the proposed improved HHO optimizer is checked through a comparison with other swarm intelligence methods in typical benchmark problems. Moreover, the experimental results of form deviation-zone evaluation on primitive geometries show that the improved method can accurately solve various form deviations, providing an effective general solution for primitive geometries in the manufacturing and metrology fields.

[Display omitted] • Over smoothing of filtering is identified as one of the major sources of on-machine compensation in fabrication of structured surface. • A novel on-machine profile error evaluation and compensation strategy based on anisotropic diffusion filter is proposed. • The proposed method controlled the form error of high aspect ratio structured surface at the scale of submicron. Structured surfaces with high aspect ratio are promising in optical components, healthcare devices, and microelectronics. A preferable method to create precise structured surfaces is using single point diamond turning with on-machine surface measurement (OMSM). However, fabricating these surfaces often pose challenges due to steep gradients and discontinuous slopes, leading to significant form errors in machining. We propose an innovative solution by employing partial differential equation (PDE) filtration in a closed loop compensation process to enhance form accuracy and surface roughness compared to traditional methods. We tackle the problem of over-smoothing induced profile error encountered with traditional Gaussian filters. The proposed compensation strategy adapts to surface curvature and reduces instrument noise during on-machine measurements. Experimental of fabricating a segment spherical artefact, demonstrate improved precision. After adopting the proposed method, the form error is reduced from 1.2 µm to 0.5 µm and vibration ripples are mitigated, and a better surface finish is achieved. [ABSTRACT FROM AUTHOR]

This study investigated a novel methodology called equivalent-sphere swing grinding (ESSG) for the cup wheel grinding of large revolving aspheric and spherical surfaces. The method is proposed to improve the machining efficiency and reduce the complexity of machine tools. Different from the traditional single-point grinding of aspheric surfaces, the ESSG method developed a novel multipoint grinding process to increase the material removal rate (MRR) and reduce the wear of single abrasive grain. A structure with few axes and a wheel spindle with multi degrees of freedom simplifies the machine tools and improves the machine dynamic stiffness. The grinding process was modeled, and the feasibility for grinding aspheric and spherical surfaces was verified. The criteria for ESSG-based grinding method were established, and the wheel position and posture models were derived. The cup wheel posture was proved to have multiple options for grinding a revolving surface, in which the optimal posture can achieve the maximum number of abrasive particles involved in grinding and maximize MRR under the same wheel wear. The numerical trajectory control parameters were calculated, and a hierarchical grinding method is proposed. An experiment was conducted on a developed grinding machine prototype. The results indicate that the proposed methodology can efficiently grind paraboloid surfaces and can be extended to grinding other revolving aspheric and spherical surfaces. [ABSTRACT FROM AUTHOR]

The article presents a literature review dealing with the effect of the honing parameters on the quality of the machined parts, as well as with the recent innovations in honing processes. First, an overview about the honing and the plateau-honing processes is presented, considering the main parameters that can be varied during machining. Then, the influence of the honing parameters on surface finish, shape deviation and material removal rate is presented. Finally, some special and innovative applications of the honing process are described. For example, honing with variable kinematics allows obtaining oil grooves that are not rectilinear but curvilinear, in order to reduce the temperature of the part during machining and thus achieving better surface finish and lower shape deviation. Automation of the honing machines is useful to improve both the production and the verification process. Another innovation consists of using 3D printed tools in honing processes, which will help to obtain abrasive tools with complex shapes, for example by means of powder bed fusion processes.

This paper is concerned with the generation of numerical artefacts, that is, reference data sets, for assessing the accuracy and fitness of purpose of software for computing minimum zone (MZ, Chebyshev) associated features. We describe an algorithm for generating datasets corresponding to a pre-specified best-fit surface and form error. We use a Gaussian process model to generate form errors that are spatially correlated. The form errors can be drawn from multivariate Gaussian or rectangular distributions. For the latter case a Gaussian copula is used to construct a multivariate multivariate distribution with the pre-assigned correlation. We illustrate the data generation on MZ circle fitting problems. We also describe an approximate MZ circle fitting problem that can be solved using linear programming.

Form error is the departure of a manufactured part from its design or ideal shape, and is a key characteristic to be assessed in quality engineering in manufacturing. In practice, form errors are usually estimated from coordinate measurements involving only a finite number of measured points and the form error for the complete workpiece surface has to be inferred on the basis of these measurements. This paper is about determining whether a product meets its specifications based on its form error using a probabilistic model. Based on form error data and a product specification, the relationship between conformance testing and making decisions is established. In this paper, we define a form error model using a uniform distribution with unknown bounds, and then utilize a Bayesian approach to assign a distribution to the form error parameter and use this distribution in a conformity and risk assessment methodology to quantify the risk of incorrect decisions. The risk assessment is carried out using derived expressions of specific risks associated with product conformity. A slightly more extensive posterior model, taking into consideration the probable random effects of form errors, is discussed for the reader's interest. Numerical experiments illustrate the effectiveness of this approach by providing a decision framework to control the risks associated with making a wrong decision.

Herein, a precision measurement method is proposed to evaluate the radial, axial, and tilt error motions of rotating devices such as precision spindles. To improve the accuracy of the estimated multiple-degree-of-freedom error motion components, form error signals in the runout signals are separated and precompensated for before the calculation of the five-degrees-of-freedom error motion components. Fourier model-based multi probe error separation (MPES) techniques, which can prevent the occurrence of harmonic distortions, are applied to separate the form error signals. A three-probe method is applied to layers on the side surface of the cylindrical artifact, and a modified two-probe method is developed and applied to the upper surface. The radial, tilt, and axial error motions are calculated using the runout signals that do not contain the separated form error signals. The measurement system uses eight capacitive probes to detect the runout signals of the cylindrical artifact mounted at the center of the rotating device. To compare the proposed method with the five-probe-based conventional measuring method, an evaluation test simulation is conducted repeatedly five times. Results indicate that the proposed MPES method calculated the uncertainty using the deviation between the computed results from the existing and novel methods; additionally, the input signal in terms of the radial, tilt (layers 1 and 2), and axial error motions are ± 0. 02 , ± 0. 01 , ± 0. 00 , and ± 0. 01 μ m , respectively. It is confirmed that the undesirable effects of the form error signals are successfully removed and that the accuracies of the measured spindle error motion components improve. [ABSTRACT FROM AUTHOR]

With steadily increasing use in dimensional metrology applications, especially for delicate parts and those with complex internal features, X-ray computed tomography (XCT) has transitioned from a medical imaging tool to an inspection tool in industrial metrology. This has resulted in the demand for standardized test procedures and performance evaluation standards to enable reliable comparison of different instruments and support claims of metrological traceability. To meet these emerging needs, the American Society of Mechanical Engineers (ASME) recently released the B89.4.23 standard for performance evaluation of XCT systems. There are also ongoing efforts within the International Organization for Standardization (ISO) to develop performance evaluation documentary standards that would allow users to compare measurement performance across instruments and verify manufacturer's performance specifications. Designing these documentary standards involves identifying test procedures that are sensitive to known error sources. This paper, which is the third in a series, focuses on geometric errors associated with the detector and rotation stage of XCT instruments. Part I recommended positions of spheres in the measurement volume such that the sphere center-to-center distance error and sphere form errors are sensitive to the detector geometry errors. Part II reported similar studies on the errors associated with the rotation stage. The studies in Parts I and II only considered one position of the rotation stage and detector; i.e., the studies were conducted for a fixed measurement volume. Here, we extend these studies to include varying positions of the detector and rotation stage to study the effect of magnification. We report on the optimal placement of the stage and detector that can bring about the highest sensitivity to each error. [ABSTRACT FROM AUTHOR]

Since current studies on the leakage flow of precision couplings are based on the ideal smooth surface, neglecting the influence of geometric structures of machined surfaces, here we proposed a non-ideal geometry-based approach in this paper to perform a more accurate prediction on the fitting performance and the leakage characteristic of precision couplings. Firstly, a non-ideal geometric surface model of precision couplings is established by fractal function that characterizes both the dimensional discrepancy and the form error of key fitting surfaces, and theoretical calculation formulas based on the non-ideal geometric model are proposed afterward to predict the fitting performance and the leakage flow rate of precision couplings. Then, the influence of various factors on the leakage flow is also analyzed by the CFD approach. Simulation results and experimental results are compared to the theoretical calculation results, so the prediction approach proposed in this paper is verified to be feasible and accurate. Finally, the proposed approach is applied to the assembly analysis of spool valve of electro-hydraulic servo valve.

Form error deflects the assembly surfaces and thus greatly affects the assembly accuracy of precision mechanical systems. Based on rigid motion, this paper proposes a prediction method for assembly surface contact considering form error to improve the simulation accuracy of virtual assembly. The method estimates the assembly equilibrium state by simulating the realistic behaviour of surfaces in assembly process: Firstly, one surface is fixed and the other is transferred along the assembly direction until the first contact occurs. Then, the other surface is rotated according the assembly force and the previous contact positions to successively reach the second and third contacts. The rotation operation is repeated until the assembly equilibrium conditions are finally met. Particularly, a space slicing algorithm is put forward to achieve faster calculation of the rotation information including rotation axis, rotation direction and rotation angle. This method can be applied in the field of assembly simulation and assembly verification. At the end of this paper, an assembly case of two rectangular plates is carried out to prove the feasibility and effectiveness of the method. [ABSTRACT FROM AUTHOR]

The traditional finite element method has the advantages of strong versatility and high calculation accuracy. Thus it is widely applied in various numerical simulation problems. Although the traditional finite element method for solving the shaft-hole assembly problem can obtain better solution accuracy, the process of modeling and calculation take a long time and thus cannot meet the engineering application requirements when the equilibrium position after the assembly needs to be obtained quickly to guide the subsequent process. In this paper, an iterative method based on the spring contact model is proposed. Firstly, the actual form error of the shaft and hole is characterized by the Fourier series expansion method; Then, in the contact surface, we established a discrete spring contact model and obtained the equivalent stiffness of the coupling spring through the discrete solid model. The balance iterative calculation based on the form errors and contact deformation force can finally determine the equilibrium position after the assembly. Compared with the calculation results of the finite element model, the equilibrium position of the shaft-hole assembly can be quickly solved under the condition of sacrificing certain precision. From this aspect it can be estimated that this method has a good potential for engineering application. [ABSTRACT FROM AUTHOR]

Machining of free-form surfaces is an important place in terms of design and performance in transportation, electronics and aeronautical industry. Problems such as form error and surface roughness were frequently encountered in the manufacture of these surfaces. For the solution of the problems, reprocessing is done, which causes time and resource loss. To eliminate these losses, the parts must be produced in the desired quality at one time. In order to find out the causes of form errors and to remove the adverse effects, the distribution on the surface must be determined correctly. Form errors should be examined in a way to cover the point, region and the whole part. In this study, a surface created with B-Spline curve has been processed with different tool paths. Surfaces were scanned in 3D and form errors were determined. Point, regional and whole parts are examined and the tool path that creates minimum form error is determined. [ABSTRACT FROM AUTHOR]

Rapid prototyping (RP) is one of the most imperative advanced manufacturing techniques. RP has attracted attention in the prototyping community due to its capability of reducing the lead time of the product development. It has emerged as an alternative method to fabricate component. RP has recently shown a wide range of engineering as well as medical applications. However, dimensional accuracy, surface roughness and part strength of the component fabricated by RP technology are poorer compared to that of traditional manufacturing process. The main emphasis of authors in this research work is to describe the methodology adopted by researchers. The novelty of this work lies in the fact that it provides a systematic approach to enable potential for persons from industry as well academic users to select suitable process parameters for fabricating the component. [ABSTRACT FROM AUTHOR]

The wavy-tilt-dam (WTD) seal is considered to be one of the ideal sealing patterns used in nuclear reactor coolant pumps (RCPs). Grinding such seals with a four-axis grinder had been proposed and six grinding implementation strategies were described in our previous studies. However, another important issue is to determine the positioning accuracy of each servo axis so that the high-precision moving components can be selected properly. In the present paper, the positioning accuracy analysis is carried out to seek a balance between the manufacturing cost and the accuracy requirements. First, a geometric model is established for investigating the error sensitivity of each axis and setting reasonable accuracy allocation of the four axes. Subsequently, the combined influence of all four axes is assessed based on multi-body system (MBS) theory and homogeneous transformation matrix (HTM). According to the results calculated, positioning errors of the X-axis, Z-axis, B-axis, and C-axis within ±10 μm, ±0.1 μm, ±1 arcsec and ±60 arcsec are acceptable, respectively. Meanwhile, the form error calculated of the ground wavy face is no more than 109.74 nm. It is indicated that the accuracy level of the moving components is achievable by modern manufacturing techniques. The present paper is expected to serve as a theoretical basis for the design and development of the four-axis grinder.

This article analyzes the advantages of thin-walled steel cylindrical structures obtained by means of rolling and emphasizes the important role of technological heredity laws at all stages of their production. The authors estimate the state-of-the-art of thin-walled pipes production, analyze technical requirements for their quality and highlight the connection between the technological heredity and steel thin-walled pipes quality indicators. The initial ovality and curvature of steel billet axis, inherited from rolling or extrusion and fixing forces occurring under any technological influence cause billet deformation and a centering error before machining, assembling or controlling stages. Functioning of steel thin-walled cylindrical billets is substantially determined by the accuracy of their geometrical parameters, with wall thickness being the dominating one. The results of the statistical analysis of key geometrical parameters' accuracy have shown that the outer diameter of thin-walled steel pipes has the lowest accuracy. Determination of error type by means of harmonious analysis has given grounds to assume that they are caused by technological system deformations. The research of technological system rigidity has shown that the billet and the mandrel are the "weakest" points, while billet axis' and walls' deformations play the dominating role in causing the overall processing error. Therefore the authors have experimentally investigated the rigidity of machines and devices. It has been established that form errors in longitudinal and cross sections are formed as a result of a joint deflection of steel thin-walled billet axis together with the mandrel. The billet wall deflection during machining also plays a significant role. Rigidity research of mandrels of various types has shown that billet form errors in the longitudinal direction are connected with the couplings in mandrels' structures. Another feature of mandrels' influence on the accuracy of processing is such a specific error as a non-uniformly focused ellipse in the cross-section. This phenomenon is explained by changing rigidity of the mandrel in various radial directions. [ABSTRACT FROM AUTHOR]

• Three probes target a measured section and two probes target two fixed sections. • Eccentricity of each sectional profile is detected by an error separation model. • The detected eccentricity vector is based on a fixed spatial straight line. • Robust immunity to interferences is obtained by the non-cumulative calculation. • A cylindrical profile is measured and reconstructed with accuracy and precision. This study focuses on developing a new error separation technique for the in situ measurement and reconstruction of cylindrical profile. Based on a five-point system proposed, the center vectors of the least squares circle in the cross-sectional profile of the cylinder can are accurately extracted by the error separation model. The vectors are based on a spatial straight line that connects two least squares centers of the fixed cross-sectional profiles, which makes the double integration calculations avoided and the ability to resist interference improved. A cylindrical profile conforming to the mathematical definition can be reconstructed for cylindricity error evaluation. Theories, numerical validations and experiments verified that the spindle's radial and tilt error motions as well as the probe carriage's straightness deviations are all removed. This innovative technique solved a crucial problem regarding the accurate and high-precision reconstruction of a cylindrical profile in the in situ measurement. [ABSTRACT FROM AUTHOR]

A three-probe error separation technique with a novel V-block for measuring and reconstructing a cylindrical profile is presented. The V-block has two tandem V-shaped planes and three displacement probes mounted in one section. During the measurement, the V-block is put onto the measured cylinder, and the two V-shaped planes contact with the cylinder when the cylinder rotates, which make the measurement of cylindrical profile immune to the radial error motions of the spindle. Three probes target each cross-section of the cylinder to collect the data. From the outputs of the probes, the least squares circle center vector of each cross-section is determined via an error separation model built in accordance with the respective relationships of the cross-sectional profiles of the cylinder and error motions of the V-block. Theoretical analysis and numerical validations proved that this technique can accurately detect the median line profile of the cylinder, and the anti-interference capability can be moderately improved by the modified error separation models based on two measuring strategies. This technique realized theoretically full harmonic error separation with the minimum number of probes, accurately detected the spatial median line of the cylinder. Further, high-precision reconstruction of the cylindrical profile was achieved. Integrating the V-block with a laser measurement system can yield a portable system for in-situ measurement cylindricity. It is foreseeable that this technique will garner more attention for future applications. •Cylindricity is measured by three-probe error separation technique with a novel V-block. • Measurement is independent of error motions of in-situ spindle and workbench. • Full harmonics error separation is realized with the minimum number of probes. • Median line profile and cylindrical profile are detected precisely by two strategies. • Portable system can be achieved by integration with laser measurement. [ABSTRACT FROM AUTHOR]

The development of standards for evaluating the performance of X-ray computed tomography (XCT) instruments is ongoing within the American Society of Mechanical Engineers (ASME) and the International Organization for Standardization (ISO) working committees. A key challenge in developing documentary standards is to identify test procedures that are sensitive to known error sources. In Part I of this work, we described the effect of geometry errors associated with the detector and determined their influence through simulations on sphere center-to-center distance errors and sphere form errors for spheres located in the tomographically reconstructed measurement volume. We also introduced a new simulation method, the single-point ray tracing method, to efficiently perform the distance and form error computations and presented data validating the method. In this second part, also based on simulation studies, we describe the effect of errors associated with the rotation stage on sphere center-to-center distance errors and sphere form errors for spheres located in the tomographically reconstructed measurement volume. We recommend optimal sphere center locations that are most sensitive to rotation stage errors for consideration by documentary standards committees in the development of test procedures for performance evaluation. [ABSTRACT FROM AUTHOR]

X-ray computed tomography (XCT), long used in medical imaging and defect inspection, is now increasingly used for dimensional measurements of geometrical features in engineering components. With widespread use of XCT instruments, there is growing need for the development of standardized test procedures to verify manufacturer specifications and provide pathways to establish metrological traceability. As technical committees within the American Society of Mechanical Engineers (ASME) and the International Organization for Standardization (ISO) are developing documentary standards that include test procedures that are sensitive to all known error sources, we report on work exploring one set of error sources, instrument geometry errors, and their effect on dimensional measurements. In particular, we studied detector and rotation stage errors in cone-beam XCT instruments and determined their influence on sphere center-to-center distance errors and sphere form errors for spheres located in the tomographically reconstructed measurement volume. We developed a novel method, called the single-point ray tracing method, that allows for efficient determination of the sphere center-to-center distance error and sphere form error in the presence of each of the different geometry errors in an XCT instrument. In Part I of this work, we (1) describe the single-point ray tracing method, (2) discuss optimal placement of spheres so that sphere center-to-center distance errors and sphere form errors are sensitive to the different detector geometry errors, and (3) present data validating our method against the more conventional radiograph-based tomographic reconstruction method. In Part II of this work, we discuss optimal placement of spheres so that sphere center-to-center distance errors and sphere form errors are sensitive to error sources associated with the rotation stage. This work is in support of ongoing standards development activity within ASME and ISO for XCT performance evaluation. [ABSTRACT FROM AUTHOR]

The evaluation of contouring error is important for multi-axis CNC machines because the tolerance specifications of manufactured parts are directly affected by contouring error. One of the fundamental quality inspections to verify that a manufactured part meets the expected tolerance is via form error evaluations. However, the existing estimation methods of contouring error are based on the position tolerance requirements. To meet the form tolerance requirements for the parts, this paper focuses on developing a high-accuracy estimation method of contouring error that is not related to a datum (ND-contouring error). In the proposed estimation method, at first, the minimum zone tolerance (MZT) method is used to transform the ideal tool tip path to match the actual one. Subsequently, by comparing the position and orientation between the actual point and the nearest point on the transformed ideal tool path, the ND-contouring error and orientation contouring error of the tool can be estimated, respectively. In addition, the difference between the proposed estimation method and previous evaluation methods is comparatively analyzed. Finally, simulations and experiments are conducted by applying the S-shaped and B-shaped machining trajectories, respectively, and the results all verify the estimation accuracy of the ND-contouring error estimation method. By adoption of compensation based on the ND-contouring error estimation, the contouring error could be significantly reduced, which will improve the quality of parts. [ABSTRACT FROM AUTHOR]

Robotic assisted milling is a process where a robot supports a workpiece while a machine tool cuts the workpiece. It can be used to suppress vibrations and minimize form errors in thin wall workpieces. In this paper, form error on a workpiece is simulated using a static force model, a frequency domain model and a hybrid model while a robot supports the workpiece from the other side. Machining results show that assistance of the robot has a considerable effect of the magnitude of form errors. Hence, support force should be carefully selected by simulation before machining. Finally, simulation results show that hybrid model gives the best fit among those three models. [ABSTRACT FROM AUTHOR]

Highlights • Influence of measurement parameters on roundness measurement results was studied. • Simultaneous variation of several factors at a time was carried out. • An empirical model has been developed to predict the standard uncertainty of measurement at different conditions. Abstract Roundness/Circularity is commonly measured using dedicated Roundness Measuring Instruments. In this study, an attempt has been made to quantify the effect of potential factors causing measurement uncertainty in such instruments. Number of sampling points, method of initial setup, rotary table speed, diameter and form error of the specimen selected for measurement are the factors which have been studied. The specimen chosen for the measurement was the poppet valve for four stroke internal combustion engines. A designed experiment was carried out and an empirical model to predict the measurement uncertainty arrived at. [ABSTRACT FROM AUTHOR]

An enhanced time-domain simulation method of cutter/workpiece dynamic engagement during milling process is proposed in this article, which comprehensively considers the effect of multi-order modal characteristics of cutter system and cutter runout including offset and inclination. Based on the cutter dynamic displacement response, this article further presents the machined surface reconstruction algorithm and evaluation method for the form error. This research systematically studies and compares the calculation accuracy between the proposed method and other previous three kinds of methods. The effectiveness of the proposed method has been verified by a series of milling experiments successfully. By comparing with the other three methods, the proposed method shows a high calculation performance, especially under the milling condition with a large axial depth of cut and low damping or stiffness of cutter system. Besides, the results indicate that the form error has a strong dependence characteristic on the milling parameters, particularly on spindle speed. Additionally, cutter runout would easily cause over cut phenomenon on the machined surface and seriously deteriorate the surface roughness. [ABSTRACT FROM AUTHOR]