Manufacturing Errors Research Articles

Duality for robust multi-dimensional vector variational control problem under invexity

This paper presents a multi-dimensional vector variational control problem wherein constraints are comprised of first order partial derivatives. As the optimization problems may contain uncertainties driven by measurement and manufacturing errors, erroneous information, irregularities, or perturbations, so the parameter’s randomness is assumed to be in the form of an uncertainty set. Firstly, the sufficient efficiency conditions are demonstrated for the problem under consideration. Then, the Wolfe type and Mond Weir type duals of the primal problem have been formulated. As in multi objective optimization models, attainment of efficient or weak efficient is the primary aim, thus the important robust duality theorems viz. weak, strong and strict converse duality theorems have been established under invexity conditions for Wolfe type dual. An example is also provided to illustrate the weak duality theorem. Thereafter, the duality results for Mond Weir type duals have been obtained under weaker invexity assumptions on involved functionals. This work extends the previously studied results on control problems and hence seeks application in diverse fields.

A novel APA model integrating manufacturing errors and barycenter characteristic for assembly unbalance optimization

A novel APA model integrating manufacturing errors and barycenter characteristic for assembly unbalance optimization

Mesh Load Factor Uncertainty Analysis in a 5‐MW Wind Turbine Planetary Gearbox Affected by Inherent Manufacturing Errors

ABSTRACTThe current work focuses on the study of the uncertainty related to the manufacturing process of gears for 5‐MW planetary transmissions aimed to the wind generator industry. With this objective, the Monte Carlo method is the employed tool to analyse the influence that selected manufacturing errors have in the performance of these planetary transmissions, more precisely in its mesh load factor. In more detail, the selected manufacturing errors are tangential pinhole position and tooth thickness errors, following the tolerances set by the DIN 3967. This study provides the probability distributions of mesh load factor values related to the size of the manufacturing errors in the transmission. Moreover, both kinds of errors are included together in numerous different planetary transmissions, and the probability distribution functions are also obtained for these. The results lead to relevant conclusions related to the influence of these errors in the performance of these transmissions and their durability and cost‐effectiveness.

The Effects of Manufacturing Errors on the Performance of Acoustic Metamaterial Lenses Operating in the MHz Regime

This article explores the use of acoustical metamaterials to design lenses in the megahertz frequency range of relevance to applications in nondestructive testing and medical imaging. In particular, the effect of manufacturing errors on their focusing performance is quantified. A rapid method for including manufacturing errors is described and this is used to perform Monte Carlo simulations of wave pressure fields from lenses with manufacturing errors. In this process, the required time delay distribution for a target focal length is calculated and the acoustical lenses with a chosen unit cell type are designed. Manufacturing errors of the unit cells are then added, considering their statistical properties and a large number of realizations. As an example, an acoustical lens with a focal length of 76 mm at a frequency of 1 MHz is designed using three different unit cell types: steel cross unit cell, resin circular void unit cell, and silicone–resin layered unit cell. Finally, the resulting acoustic pressure fields are computed using a Huygens’ principle model to assess the effects of manufacturing errors on lens performance, i.e., the focal length and the size of the focal spot. It is shown that the performance of lenses consisting of silicone–resin layered units is less affected by the manufacturing errors than for lenses constructed with the other unit cells. This study paves the way for selecting a suitable combination of metamaterial unit cell and manufacturing method to enable acceptable lens imaging performance.

Generalization Process of the Integrated Mathematical Model Created for the Development of the Production Geometry of Complicated Surfaces

Computer modelling of technical constructions is increasingly carried out using software that includes more detailed knowledge, which requires an increase in the level as well as an expansion of the scope of the geometric knowledge. A significant part of motion transmission mechanisms are worm drive pairs, for which the separation of the parts dealing with the theoretical and practical problems found in the literature can be experienced in numerous instances. Due to the different technical features, in many cases the helical surfaces are not designed and manufactured in a geometrically correct way, or the best solution is not the compulsory chosen. The geometric model describing the production process of the worm surfaces provides the basis for examining the deviation between the surface mathematically determined by the designer and the surface produced. An integrated mathematical kinematic model was developed for the production geometrical analysis of the elements of cylindrical and conical worm gear drive pairs for machining with a traditional thread grinding machine, which causes a serious pitch fluctuating error among several other problems in the case of machining the conical worm. Modelling of the production process of surfaces and the simultaneous study of the manufacturing errors is basically performed with the toolbox of descriptive geometry, including the use of the projective invariants. Knowing the inheritance of the invariants of projective geometry, the aim was the mathematical generalization of the integrated model and the creation of a projective relationship between the reference surfaces of conical and cylindrical spiral surfaces. As a result, the improved constructive geometric model was created, in which the method of analytically creating the projective geometric relationship between the reference surfaces of conical and cylindrical helicoid surfaces has been described for the first time in this article. This procedure is considered the most important result of the present article. Another significance of the further development presented is that during production of the conical helicoid surface, the thread pitch fluctuation has been eliminated. The results obtained, consisting of an improved geometric model, lead to a new geometry of the technological environment regarding the relative position of the cutting tool and the workpiece as well as the relative motion between them.

Wideband compact 3-dB microstrip power divider for L- and S-band applications

Abstract This paper presents the analysis, design, built and testing of a new compact 3 dB power divider operating across a wideband frequency range, with a 2.56 GHz center frequency. The proposed divider, consisting of three ports, is constructed using an FR4 substrate, with overall dimensions of 45 × 40 × 1 mm3. The frequencies with the best S21 and S31 results are recorded with a magnitude of −3.04 dB at 2.56 GHz. The simulated input match (S11) displays nearly −30 dB at 2.56 GHz, with a −10 dB bandwidth extending from 1 to 4 GHz, resulting in a total bandwidth of 3 GHz. Hence, the proposed power divider emerges as a strong candidate for applications in both the L- and S-bands. The measured data exhibit strong agreement with the simulation results. The originality of this study lies in achieving high performance within such compact dimensions at an affordable cost, thereby eliminating the complexity that can lead to manufacturing errors. Additionally, it is demonstrated through a comparative table that the proposed power divider exhibits superiority over similar ones found in the literature.

Study on Error Influence Analysis of an Annular Cable Bearing-Grid Structure

Manufacturing errors of cable length, external node coordinates and tension force by the passive tension method are inevitable, which will inevitably affect the prestressing of cable bearing-grid structures, while existing studies lack the error analysis of error influences in this area. This paper proposes a method for analyzing random errors in constructing annular cable bearing-grid structures. An error control index and a normal distribution-based random error model, considering the impact of cable and ring beam length errors on cable force, were established afterwards. Taking the roof of the Qatar Education City Stadium as an example, the influence of the length errors of the radial cable, ring cable, and outer pressure ring beam on the structural cable force and stress level was analyzed, and the coupling error effect analysis was carried out. The results show that ring cable force and radial cable force are less affected by the length error of each other’s cables, while they are more affected by the length error of the outer ring beam. Stress levels exhibit greater sensitivity to outer ring beam errors compared to cable length errors. As the error limits of outer ring beam increase, radial and ring cable error ratios and outer ring beam stress errors also rise.

High Azimuthal Mode Selectivity of a Cavity with Mode-Joining Corrugations for High-Harmonic Gyrotrons

Mode-joining longitudinal corrugations are studied as a means of high azimuthal mode selectivity for cavities of high-harmonic terahertz gyrotrons. Their number dictates the choice of the jointed operating mode, which has a form of strongly coupled co- and counter-rotating azimuthal harmonics. It is found that the distinctive feature of this mode is a weak dependence of eigenvalue and ohmic losses on corrugation size. First, this favors the use of mode-joining corrugations with variable depth for efficient suppression of all competing modes by both diffractive and ohmic losses in the gyrotron cavity. Second, this provides a good robustness of gyrotron performance against manufacturing errors in the size of corrugations and only a minor conversion of the operating mode to spurious modes at junctions of the corrugated cavity with smooth-walled waveguides. The beneficial properties of mode-joining corrugations are demonstrated by a cavity design for a gyrotron operated in the second-harmonic TE±9,4 and third-harmonic TE±18,4 modes at 398 GHz and 593 GHz, respectively.

Effects of periodic long-wave deviations on the dynamic behaviors of spur gear systems

Noise reduction plays a major role in the drive train of motor vehicles operating at higher speeds. Long-wave deviations of gear systems related to manufacturing and assembly errors, such as tooth pitch deviation and geometric eccentricity, exhibit circumferential variations and have been demonstrated to be significant contributors to noise generation. However, a comprehensive and effective model that considers multiple long-wave deviations simultaneously has seldom been studied. To fill this gap, a new numerical model of spur gear systems with long-wave deviations is established, in which the coupling effects of both tooth pitch deviation and geometric eccentricity are taken into consideration. A time-varying mesh stiffness (TVMS) analytical model for spur gear pairs is established, which considers the relationship of errors between pitch deviation and eccentricity. The time-varying contact state of the gear pair under periodic long-wave deviations is also analyzed. A translation-torsion coupled dynamic model is established to investigate the excitation behavior of gear pairs with periodic long-wave deviations. The accuracy of the TVMS and the dynamic model is verified through comparisons with reference and experimental results. Results show that gear pairs with long-wave deviations exhibit periodic fluctuations in TVMS compared to ideal gear pairs, accompanied by phase differences. The mesh stiffness impact phenomenon becomes less pronounced for higher gear precision under lower-load conditions. Conversely, the periodic vibration characteristics induced by eccentricity become less prominent for the lower gear precision level. The excitation behavior of the gear pair with pitch deviation is masked by eccentricity at lower rotational orders, but it still dominates at higher rotational orders. This method can predict the dynamic characteristics of gear transmission systems with periodic long-wave deviations, providing theoretical guidance for reducing the vibration and noise levels.

Optimization design of assembly sequence for the proton exchange membrane fuel cell stacks with dimensional errors

Proton exchange membrane fuel cell (PEMFC) stacks are assembled by numerous bipolar plates (BPPs) and membrane electrode assemblies (MEAs). Component manufacturing errors are inevitably caused during the production process and brought into the stack, affecting the mechanical consistency of every cell. Aiming to improve the uniformity of the assembled stack effectively, this paper establishes a novel assembly deviation model based on the asymptotic homogenization (AH) method and proposes an assembly sequence optimization approach for the stack with dimensional errors using the genetic algorithm. The results reveal that dimensional errors significantly affect the equivalent mechanical properties of the stack. Reasonable matching of components with different types of dimensional errors is an effective method to avoid the cumulative negative impacts on the mechanical behavior of the stack. Statistically, the optimization of the assembly sequence can improve contact pressure uniformity in a 10-cell stack by more than 9.00%, while reducing the maximum contact pressure by 15.55%. This methodology is also applicable to improving the assembly uniformity of other stacked structures.

Impact of random geometric errors in an elliptical superconducting magnet with application to a compact heavy-ion synchrotron

A compact heavy-ion synchrotron is under development for next-generation cancer therapy. A superconducting magnet is designed with a main dipole field of 3.5 T and a field error less than 5 × 10−4 to maintain compactness. The coil is wound directly with monolithic Nb-Ti wire on a curved elliptical mandrel, comprising 22 laminated layers to achieve the desired magnetic field. Given the critical need for field quality, it is imperative to determine the tolerance of coil fabrication and to devise a method to eliminate field error during the design stage. This paper presents a numerical investigation of possible random geometric errors stemming from fabrication and assembly tolerances in a curved elliptical superconducting magnet. We first provide an analytical formulation derived in a complex plane to estimate the field error of a straight elliptical coil. We then conduct a Monte Carlo simulation to assess cases involving misalignment of individual wires and coil block sectors. Additionally, we compare simulation results with field measurements obtained from a short model magnet tested previously to predict potential random errors in manufacturing. Finally, we calculate the beam dynamic aperture to assess the effects of random geometric errors on beam loss using Monte Carlo simulation results. This method enables the prediction of tolerances for fabricating high-quality high-field magnets and aids in making design decisions concerning the utilization of active shim coils.

Modeling of CNC machine tool line rail assembly accuracy and its control method

Aiming at the linear guide assembly process, due to the preload load caused by the assembly deformation mechanism is not clear resulting in the guide assembly straightness is difficult to predict the problem. In this paper, based on the establishment of linear guide assembly deformation model, the ideal and actual conditions of the guide assembly deformation is discussed. Secondly, considering the influence of manufacturing error of the guide rail mounting surface on the guide rail assembly accuracy, it puts forward the integrated assembly deformation and manufacturing error of the guide rail assembly straightness error prediction model, and puts forward the control method of the guide rail assembly accuracy based on the assembly deformation and the inverse repair manufacturing error. Finally, the experimental bench is built and the accuracy of the theoretical model and accuracy control method is verified through experiments , and the results show that the straightness error of the guideway assembly is reduced by .

Back propagation neural network model for controlling artificial rocks petrophysical properties during manufacturing process

Artificial rocks are increasingly used in experiments, and it is important to make artificial rocks’ petrophysical properties similar to real rocks to obtain more valuable results. The effect of widely used five factors, grain size (GS), grain size distribution (GSD), mass fraction of cementing agent (MC), pressing pressure (PP), and pressing time (PT), on artificial rock petrophysical properties are analyzed. Three factors, GS, MC, and PP, which are suitable for establishing a quantitative model are opted. The relationships of 80 rock plugs’ petrophysical properties and manufacturing factors are studied, which indicates MC and PP are negatively correlated with porosity and permeability, and GS has a significant effect on permeability but little effect on porosity. Furthermore, a novel back propagation (BP) neural network model is proposed, which can be used to determine factor values during artificial rock manufacturing process. A series of artificial core plugs are manufactured relying on manufacturing factor values calculated by the BP neural network model, and their petrophysical properties are tested and compared with design petrophysical properties value to verify the model. Verification results show that comprehensive average error of porosity and permeability of artificial rock, including calculating error and manufacturing error, is 2.38 and 18.68%, respectively.

Design of Gearings from Involute-Bevel Gears

The article presents formulas for determining the dimensions of involute-bevel gears and the gearings composed of them. It examines the most general cases of gearings formation, consisting of two involute-bevel gears with crossing axes (hyperboloid gearings), with intersecting axes (bevel gearings), and with parallel axes (cylindrical gearings). Gearings composed of involute-bevel gears have design, technological, and operational advantages compared to gearings composed of conventional cylindrical and bevel gears. The use of involute-bevel gearings with crossing axes allows for achieving the required contact character of the teeth from localized contact to linear contact, reducing sensitivity to manufacturing and assembly errors, and increasing the load capacity of the gearing compared to helical gearings from cylindrical gears. Bevel gearings with involute-bevel gears allow for the creation of gearings with any desired small shaft angles, which is difficult to achieve with conventional bevel gears. The use of internal meshing bevel gearings with modified tooth profiles in planetary reducers allows for gearings comparable to harmonic drives in terms of power and kinematic characteristics, but with a higher operational life. The use of involute-bevel gears in cylindrical gearings improves the smoothness of the mechanism and allows for adjusting the center distance and backlash in the meshing, making them suitable for backlash-free drives. By combining the taper angles of the gears and the inclination of the teeth, it is possible to create a one-way rotation mechanism - a freewheel mechanism. Modern CAD systems do not take into account the geometry features of gearings composed of involute-bevel gears, which limits their application in technology. The article proposes an algorithm for calculating the main geometric parameters of gearings composed of involute-bevel gears with arbitrary axis placement in space. Examples of geometric calculations of various types of gearings based on the proposed algorithm are provided.

Design of coma-free Hettrick-Underwood type spectrometers for high energy resolution RIXS experimental station.

The Hettrick-Underwood (HU) type design, consisting of a pre-focusing mirror and a varied-line-spacing planar grating (VLS-PG), for the high resolution resonant inelastic x-ray scattering spectrometer is considered. The light path of the HU design is analyzed, and the analytical functions determining the groove parameters of VLS-grating are given. Efforts are made to compare the different choices of the pre-focusing mirrors, circular cylindrical (HU-CM) and elliptical cylindrical (HU-EM). Although the HU-EM type offers great tuning properties with variable-included-angle, it imposes high requirement on the optical element manufacturing accuracy, while the HU-CM type design couples the coma contributions from the pre-mirror and the grating, allowing for mutual compensation of the manufacturing errors of the two optical elements.

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

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

Robot error compensation strategy based on error sensitivity

Abstract Due to the errors in manufacturing and assembly, there are differences between the actual model and the theoretical model of the robot, which affects the positioning accuracy of the robot end-effector. In order to improve the accuracy of robot end-effector position, a robot error compensation strategy based on error sensitivity is proposed.Firstly, the robot kinematic model is established by Denavit-Hartenberg (D-H) method, and the sensitivity of end-effector position error is analyzed. According to the influence degree of different kinematic parameters on the robot end-effector position accuracy in the whole workspace, different weights are given to different kinematic parameters. {\color{red}Secondly, the kinematic error model is established, and the redundancy of the error parameter matrix is analyzed to obtain an independent error model. Thirdly, based on the error sensitivity analysis, a Weighted Levenberg-Marquard (WLM) algorithm with adaptive penalty factor is proposed, and the kinematic parameters are iteratively identified.} Finally, an error compensation experiment is carried out by using a universal serial six-degree-of-freedom robot. The experimental results show that the maximum error, mean absolute error and root mean square error of the position error on the test set are reduced by 90.75%, 89.86% and 95.64% respectively. The research in this paper provides a theoretical basis for robot end error compensation.

High-precision angle error compensation method for a Dove prism scanning system based on galvanometers.

Dove prisms suffer from angle and shift errors due to inevitable errors in manufacturing and installation, limiting their applicability in tasks requiring high-precision scanning. These errors, particularly angle errors, can significantly deform and ruin the intended scanning trajectory. Here, we propose a method for compensating the angle errors in Dove prisms using galvanometers. The method first determines the angle error by analyzing the distorted scanning trajectory. Subsequently, by synchronizing the galvanometers with the Dove prism rotation, the galvanometers dynamically correct the angle error at each rotation angle. This approach eliminates the need for complex mechanical adjustment mechanisms and offers a convenient calibration process. Our experiments demonstrate that the angle error can be adjusted to be below 17 µrad under the described conditions. By enabling high-precision scanning, this method has the potential to broaden the application scenarios of Dove prisms in various fields.

Dynamic analysis of planetary gear transmission based on Lagrange interpolation polynomials

Abstract This paper proposes a novel dynamic model considering manufacturing errors and eccentricity errors to analyze the dynamics of planetary gear transmission (PGT). The dynamic model is established based on the fractional-order calculus (FOC) and solved by an enhanced fourth-order Lagrange interpolation polynomials (LIP) method. Three numerical examples and the vibration experiments of planetary gear transmission are employed for verification. The comparison results indicate that the proposed solution method has higher solution accuracy and efficient than the existing algorithms in solving fractional equations, and the relative errors of the proposed solution method in three examples are 0.32%, 0.78% and 0.16%, respectively. The proposed dynamic model of PGT has better agreement with the experimentally measured signal compared with the integer-order dynamic model, and the maximum error and average error of the characteristic frequency amplitude between the proposed dynamic model and the measured signal are 4.76% and 3.57%, respectively. The proposed method contributes to the theoretical foundation for the signal monitoring of PGT.

Multi-dimensional error figuring model for ion beams in X-ray mirrors.

X-ray mirrors are core optical elements in synchrotron light sources, which are typically figured by ion beams. However, traditional ion beam figuring (IBF) methods cannot effectively correct both the height and 2D slope errors. Thus, what we believe to be a novel multi-dimensional error figuring model (MEFM) is proposed to integrate the height and 2D slope errors into a linear system of equations for simultaneous multi-dimensional error convergence. The weight values are determined based on specific manufacturing errors. The simulation results show that MEFM can achieve lower 2D slope and height errors than a single height or 2D slope errors in the figuring method. The power spectral density (PSD) curves before and after simulated figuring demonstrate that the low- and mid-frequency errors are corrected simultaneously. Figuring experiments on a 270 mm × 15 mm X-ray reflector showed that the height and 2D slope errors effectively converged. The results of the PSD curves indicate that MEFM is more effective than the traditional height figuring model in correcting mid-frequency errors, which further proves the validity of the solution model. This study provides an algorithmic reference for the IBF of ultra-high precision X-ray reflectors, thereby promoting the development of physics, medicine, materials, and other fields.