Applied Sciences

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17 pages, 2508 KiB

Open AccessArticle

Speeding up Statistical Tolerance Analysis to Real Time

by Peter Grohmann and Michael S. J. Walter

Appl. Sci. 2021, 11(9), 4207; https://doi.org/10.3390/app11094207 - 5 May 2021

Cited by 5 | Viewed by 2772

Statistical tolerance analysis based on Monte Carlo simulation can be applied to obtain a cost-optimized tolerance specification that satisfies both the cost and quality requirements associated with manufacturing. However, this process requires time-consuming computations. We found that an implementation that uses the graphics [...] Read more.

Statistical tolerance analysis based on Monte Carlo simulation can be applied to obtain a cost-optimized tolerance specification that satisfies both the cost and quality requirements associated with manufacturing. However, this process requires time-consuming computations. We found that an implementation that uses the graphics processing unit (GPU) for vector-chain-based statistical tolerance analysis scales better with increasing sample size than a similar implementation on the central processing unit (CPU). Furthermore, we identified a significant potential for reducing runtime by using array vectorization with NumPy, the proper selection of row- and column- major order, and the use of single precision floating-point numbers for the GPU implementation. In conclusion, we present open source statistical tolerance analysis and statistical tolerance synthesis approaches with Python that can be used to improve existing workflows to real time on regular desktop computers. Full article

(This article belongs to the Special Issue Mechanical Tolerance Analysis in the Era of Industry 4.0)

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15 pages, 1907 KiB

Open AccessFeature PaperArticle

Statistical Tolerance Analysis—A Survey on Awareness, Use and Need in German Industry

by Michael S. J. Walter, Christina Klein, Björn Heling and Sandro Wartzack

Appl. Sci. 2021, 11(6), 2622; https://doi.org/10.3390/app11062622 - 16 Mar 2021

Cited by 10 | Viewed by 3800

Abstract

The importance of geometric deviations of components for the aesthetic and functional quality of products has been undisputed for decades. So, it is not surprising that not only have numerous researchers devoted themselves to this field, but also commercial software tools for the [...] Read more.

The importance of geometric deviations of components for the aesthetic and functional quality of products has been undisputed for decades. So, it is not surprising that not only have numerous researchers devoted themselves to this field, but also commercial software tools for the analysis and optimization of tolerance specifications (currently already fully integrated in 3D-CAD systems) have been available for around 30 years. However, it is even more surprising that the well-founded specification of tolerances and their analysis using a so-called statistical tolerance analysis are only established in a few companies. There is thus a contradiction between the proclaimed relevance of tolerances and their actual consideration in everyday business life. Thus, the question of the significance of geometric deviations and tolerances as well as the use of statistical tolerance analysis arises. Therefore, a survey among 102 German companies was carried out. The results are presented and discussed in this paper. Full article

(This article belongs to the Special Issue Mechanical Tolerance Analysis in the Era of Industry 4.0)

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30 pages, 9853 KiB

Open AccessArticle

Investigating the Dimensional and Geometric Accuracy of Laser-Based Powder Bed Fusion of PA2200 (PA12): Experiment Design and Execution

by Torbjørn Langedahl Leirmo and Oleksandr Semeniuta

Appl. Sci. 2021, 11(5), 2031; https://doi.org/10.3390/app11052031 - 25 Feb 2021

Cited by 6 | Viewed by 2717

Abstract

Variation management in additive manufacturing (AM) is progressively more important as technologies are implemented in industrial manufacturing systems; hence massive research efforts are focused on the modeling and optimization of process parameters and the effect on final part quality. These efforts are, however, [...] Read more.

Variation management in additive manufacturing (AM) is progressively more important as technologies are implemented in industrial manufacturing systems; hence massive research efforts are focused on the modeling and optimization of process parameters and the effect on final part quality. These efforts are, however, hampered by the very problem they are seeking to solve, as conclusions are weakened by poor validity, reliability, and repeatability. This paper details an elaborate experiment design and the subsequent execution with the aim of making the research data available without loss of validity. Test artifacts were designed and allocated to fixed positions and orientations in a grid pattern within the build chamber to facilitate rigid analysis between different builds and positions in the build chamber. A total of 507 specimens were produced over three builds by laser sintering PA12 before inspection with a coordinate measuring machine. This research demonstrates the inherent variations of laser-based powder bed fusion of polymers (LB-PBF/P) that must be considered in experiment designs to account for noise factors. In particular, the results indicate that the position in the xy-plane has a major influence on the geometric accuracy, while the position in the z-direction appears to be less influential. Full article

(This article belongs to the Special Issue Mechanical Tolerance Analysis in the Era of Industry 4.0)

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15 pages, 2469 KiB

Open AccessArticle

A Unique Model to Estimate Geometric Deviations in Drilling and Milling Due to Two Uncertainty Sources

by Wilma Polini and Andrea Corrado

Appl. Sci. 2021, 11(5), 1996; https://doi.org/10.3390/app11051996 - 24 Feb 2021

Cited by 5 | Viewed by 1865

Abstract

Industry 4.0 involves the use of information and communication technologies to transform industry by intelligent networking machines and processes. The availability of big data sets from manufacturing and inspection allow for developing new and more accurate simulation models. This involves the development of [...] Read more.

Industry 4.0 involves the use of information and communication technologies to transform industry by intelligent networking machines and processes. The availability of big data sets from manufacturing and inspection allow for developing new and more accurate simulation models. This involves the development of new machining simulation models to consider the geometrical deviations of the workpiece due to the machine tool, the part datum surfaces and the fixturing equipment. This work presents a model that kinematically correlates the locator uncertainty, the form deviation on the part datum surface in contact with the locators and the volumetric uncertainty of the machine tool, with the geometric deviations of a surface due to a drilling or milling process. An analytical model was developed in a Matlab^® file to simulate the surface geometrical deviations from nominal during drilling or milling. It is new as regards the state of the art because it takes into account two sources of uncertainty. This numerical approach allows for avoiding experimental tests, with a resultant saving of time, energy and material. It was applied to drilling, face milling and contouring processes. It was proved that machine tool volumetric uncertainty influences the form deviation of the machined surface, while the locator configuration and the datum form deviation affect the orientation of the machined surface, as should be in reality. The proposed model allows us to take into account geometrical deviations of the part datum surfaces of 0.001 mm, location deviations in the locators of ± 0.03 mm and machine tool positional and rotational uncertainties of

0.01 mm

and

σ_{d} = 0.01 * \frac{π}{180} mm

, respectively. Full article

(This article belongs to the Special Issue Mechanical Tolerance Analysis in the Era of Industry 4.0)

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14 pages, 6818 KiB

Open AccessFeature PaperArticle

A Geometric Algorithm to Evaluate the Thickness Distribution of Stretched Sheets through Finite Element Analysis

by Gillo Giuliano, Andrea Corrado and Wilma Polini

Appl. Sci. 2021, 11(4), 1905; https://doi.org/10.3390/app11041905 - 22 Feb 2021

Cited by 7 | Viewed by 1829

Abstract

Industry 4.0 aims to digitalize the manufacturing process to increase the productivity and the product quality of plants. A fundamental aspect of the digitalized manufacturing processes is the simulation of the manufacturing process in order to develop its virtual representation, known as digital [...] Read more.

Industry 4.0 aims to digitalize the manufacturing process to increase the productivity and the product quality of plants. A fundamental aspect of the digitalized manufacturing processes is the simulation of the manufacturing process in order to develop its virtual representation, known as digital twin, whose purposes may be monitoring, and control. Algorithms to elaborate the simulated data in order to improve the control of the manufacturing process are very important and they need to be developed. Sheet metal forming is a widely used process to manufacture parts with a high production rate and a low cost. The thinning of the stretched sheet needs to be controlled in detail, because it is strongly connected with the product quality. This work presents a simulation model and a geometric algorithm to evaluate the thickness distribution of a sheet stretched through a forming process. In order to accurately evaluate the thickness trend, a geometric algorithm was proposed which, on the basis of the position of the nodes of the internal and external surface of the sheet, was able to evaluate the thickness value. It enables finding of the minimum value of the stretched sheet thickness. The geometric algorithm was slightly modified, in a second step of the work, to experimentally evaluate the thickness trend of a sheet stretched by a forming process; it was applied to the measurement points obtained through a coordinate measurement machine on the inner and outer surfaces of the sheet. The numerical–experimental comparison of the results shows the appropriateness of the proposed algorithm for numerical data. Full article

(This article belongs to the Special Issue Mechanical Tolerance Analysis in the Era of Industry 4.0)

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18 pages, 3843 KiB

Open AccessArticle

Statistical Tolerance Analysis of 3D-Printed Non-Assembly Mechanisms in Motion Using Empirical Predictive Models

by Paul Schaechtl, Benjamin Schleich and Sandro Wartzack

Appl. Sci. 2021, 11(4), 1860; https://doi.org/10.3390/app11041860 - 20 Feb 2021

Cited by 10 | Viewed by 3061

Abstract

Fused Deposition Modelling (FDM) enables the fabrication of entire non-assembly mechanisms within a single process step, making previously required assembly steps dispensable. Besides the advantages of FDM, the manufacturing of these mechanisms implies some shortcomings such as comparatively large joint clearances and geometric [...] Read more.

Fused Deposition Modelling (FDM) enables the fabrication of entire non-assembly mechanisms within a single process step, making previously required assembly steps dispensable. Besides the advantages of FDM, the manufacturing of these mechanisms implies some shortcomings such as comparatively large joint clearances and geometric deviations depending on machine-specific process parameters. The current state-of-the-art concerning statistical tolerance analysis lacks in providing suitable methods for the consideration of these shortcomings, especially for 3D-printed mechanisms. Therefore, this contribution presents a novel methodology for ensuring the functionality of fully functional non-assembly mechanisms in motion by means of a statistical tolerance analysis considering geometric deviations and joint clearance. The process parameters and hence the geometric deviations are considered in terms of empirical predictive models using machine learning (ML) algorithms, which are implemented in the tolerance analysis for an early estimation of tolerances and resulting joint clearances. Missing information concerning the motion behaviour of the clearance affected joints are derived by a multi-body-simulation (MBS). The exemplarily application of the methodology to a planar 8-bar mechanism shows its applicability and benefits. The presented methodology allows evaluation of the design and the chosen process parameters of 3D-printed non-assembly mechanisms through a process-oriented tolerance analysis to fully exploit the potential of Additive Manufacturing (AM) in this field along with its ambition: ‘Print first time right’. Full article

(This article belongs to the Special Issue Mechanical Tolerance Analysis in the Era of Industry 4.0)

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18 pages, 1792 KiB

Open AccessArticle

Integrated Tolerance and Fixture Layout Design for Compliant Sheet Metal Assemblies

by Abolfazl Rezaei Aderiani, Martin Hallmann, Kristina Wärmefjord, Benjamin Schleich, Rikard Söderberg and Sandro Wartzack

Appl. Sci. 2021, 11(4), 1646; https://doi.org/10.3390/app11041646 - 11 Feb 2021

Cited by 12 | Viewed by 2993

Abstract

Part tolerances and fixture layouts are two pivotal factors in the geometrical quality of a compliant assembly. The independent design and optimization of these factors for compliant assemblies have been thoroughly studied. However, this paper presents the dependency of these factors and, consequently, [...] Read more.

Part tolerances and fixture layouts are two pivotal factors in the geometrical quality of a compliant assembly. The independent design and optimization of these factors for compliant assemblies have been thoroughly studied. However, this paper presents the dependency of these factors and, consequently, the demand for an integrated design of them. A method is developed in order to address this issue by utilizing compliant variation simulation tools and evolutionary optimization algorithms. Thereby, integrated and non-integrated optimization of the tolerances and fixture layouts are conducted for an industrial sample case. The objective of this optimization is defined as minimizing the production cost while fulfilling the geometrical requirements. The results evidence the superiority of the integrated approach to the non-integrated in terms of the production cost and geometrical quality of the assemblies. Full article

(This article belongs to the Special Issue Mechanical Tolerance Analysis in the Era of Industry 4.0)

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18 pages, 2908 KiB

Open AccessArticle

On the Development of a Surrogate Modelling Toolbox for Virtual Assembly

by Manuel Kaufmann, Ira Effenberger and Marco F. Huber

Appl. Sci. 2021, 11(3), 1181; https://doi.org/10.3390/app11031181 - 27 Jan 2021

Cited by 3 | Viewed by 3883

Abstract

Virtual assembly (VA) is a method to simulate the physical assembly (PA) of scanned parts. Small local part deviations can accumulate to large assembly deviations limiting the product quality. The propagation of geometrical deviations onto the assembly is a crucial step in tolerance [...] Read more.

Virtual assembly (VA) is a method to simulate the physical assembly (PA) of scanned parts. Small local part deviations can accumulate to large assembly deviations limiting the product quality. The propagation of geometrical deviations onto the assembly is a crucial step in tolerance management to assess the assembly quality. Current approaches for VA do not sufficiently consider the physical joining process. Therefore, the propagated assembly geometry may deviate strongly from the PA. In the state of the art, only specific and complex methods for particular joining processes are known. In this paper, the concept of Surrogate Models (SMs) is introduced, representing the connection between part and assembly geometries for particular joining processes. A Surrogate Modelling Toolbox (SMT) is developed that is intended to cover the variety of joining processes by the implementation of suitable SMs. A particular SM is created by the composition of suitable Surrogate Operations (SOs). An open list of SOs is presented. The composition of a SM is studied for a laser welding process of two polymer components. The resulting VA is compared to the PA in order to validate the developed model and is quantified by the exploitation ratio R. Full article

(This article belongs to the Special Issue Mechanical Tolerance Analysis in the Era of Industry 4.0)

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17 pages, 4295 KiB

Open AccessArticle

An Unbalance Optimization Method for a Multi-Stage Rotor Based on an Assembly Error Propagation Model

by Yue Chen, Jiwen Cui and Xun Sun

Appl. Sci. 2021, 11(2), 887; https://doi.org/10.3390/app11020887 - 19 Jan 2021

Cited by 13 | Viewed by 3244

Abstract

For the assembly of a multi-stage rotor, such as an aero-engine or gas turbine, the parts need to be assembled optimally to avoid excessive unbalance. We propose a method to optimize the unbalance of a multi-stage rotor during assembly. First, we developed an [...] Read more.

For the assembly of a multi-stage rotor, such as an aero-engine or gas turbine, the parts need to be assembled optimally to avoid excessive unbalance. We propose a method to optimize the unbalance of a multi-stage rotor during assembly. First, we developed an assembly error propagation model for a multi-stage rotor. The alignment process and distribution of the screw holes of the adjacent rotors was considered for the first time. Secondly, we propose a new assembly datum for unbalance optimization to ensure consistency with the actual conditions of a dynamic balance test. Finally, the unbalance optimization of a multi-stage rotor was achieved using a genetic algorithm, and the corresponding optimal assembly orientations of rotors at different stages were also identified. The results of the simulations showed that the assembly error propagation model had high accuracy and that the genetic optimization process had good convergence. The effect of unbalance optimization was also proven with experiments. Full article

(This article belongs to the Special Issue Mechanical Tolerance Analysis in the Era of Industry 4.0)

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28 pages, 9755 KiB

Open AccessArticle

Analysis and Experimental Verification of Mechanical Errors in Nine-Link Type Double-Toggle Mold/Die Clamping Mechanisms

by Wen-Tung Chang, Wei-I Lee and Kuan-Lun Hsu

Appl. Sci. 2021, 11(2), 832; https://doi.org/10.3390/app11020832 - 17 Jan 2021

Cited by 9 | Viewed by 8498

Abstract

Nine-link type double-toggle mold/die clamping mechanisms are widely used in modern injection molding machines and die casting machines in order to provide sufficient mold/die clamping force for counteracting the pressure occurred inside molds/dies. In this paper, the analysis and experimental evaluation of mechanical [...] Read more.

Nine-link type double-toggle mold/die clamping mechanisms are widely used in modern injection molding machines and die casting machines in order to provide sufficient mold/die clamping force for counteracting the pressure occurred inside molds/dies. In this paper, the analysis and experimental evaluation of mechanical errors in nine-link type double-toggle mold/die clamping mechanisms are presented. The kinematic error equations of the output link (i.e., the moving platen) caused by dimensional errors (or tolerances) of link members are derived analytically through the concept of tolerance sensitivity analysis. Evaluation indices based on the asymmetry of the mold/die clamping mechanism caused by mechanical errors are established. A case study is then given to demonstrate the derived analytical equations and the established evaluation indices. Subsequently, a prototype for performing the experimental evaluation is conceptually designed and was actually constructed. Experiments were conducted for evaluating the quantitative influence of mechanical errors on the operating performance of the constructed mold/die clamping mechanism. According to the experimental results, response surface modelling for benefiting the constructed mold/die clamping mechanism with better operating performance could be performed. The presented research results will be helpful in the tolerance analysis and mechanical error detection of nine-link type double-toggle mold/die clamping mechanisms. Full article

(This article belongs to the Special Issue Mechanical Tolerance Analysis in the Era of Industry 4.0)

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11 pages, 3897 KiB

Open AccessArticle

Tolerancing Informatics: Towards Automatic Tolerancing Information Processing in Geometrical Variations Management

by Benjamin Schleich and Nabil Anwer

Appl. Sci. 2021, 11(1), 198; https://doi.org/10.3390/app11010198 - 28 Dec 2020

Cited by 10 | Viewed by 2918

Abstract

The management of geometrical variations throughout the product life cycle strongly relies on the gathering, processing, sharing and dissemination of tolerancing information and knowledge. While today, this is performed with many manual interventions, new means for automatic information processing are required in future [...] Read more.

The management of geometrical variations throughout the product life cycle strongly relies on the gathering, processing, sharing and dissemination of tolerancing information and knowledge. While today, this is performed with many manual interventions, new means for automatic information processing are required in future geometrical variations management to make full use of new digitalization paradigms, such as industry 4.0 and digital twins. To achieve this, the paper proposes the term tolerancing informatics and investigates new concepts and means for automatic information processing, novel information sharing workflows as well as the integration of tools for next generation geometrical variations management. In this regard, the main aim of the paper is to structure existing tolerancing informatics workflows as well as to derive future research potentials and challenges in this domain. The novelty of the paper can be found in providing a comprehensive overview of tolerancing informatics as an important enabler for future geometrical variations management. Full article

(This article belongs to the Special Issue Mechanical Tolerance Analysis in the Era of Industry 4.0)

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20 pages, 3615 KiB

Open AccessArticle

Multidomain Simulation Model for Analysis of Geometric Variation and Productivity in Multi-Stage Assembly Systems

by Sergio Benavent Nácher, Pedro Rosado Castellano, Fernando Romero Subirón and José V. Abellán-Nebot

Appl. Sci. 2020, 10(18), 6606; https://doi.org/10.3390/app10186606 - 22 Sep 2020

Cited by 6 | Viewed by 2790

Abstract

Nowadays, the new era of industry 4.0 is forcing manufacturers to develop models and methods for managing the geometric variation of a final product in complex manufacturing environments, such as multistage manufacturing systems. The stream of variation model has been successfully applied to [...] Read more.

Nowadays, the new era of industry 4.0 is forcing manufacturers to develop models and methods for managing the geometric variation of a final product in complex manufacturing environments, such as multistage manufacturing systems. The stream of variation model has been successfully applied to manage product geometric variation in these systems, but there is a lack of research studying its application together with the material and order flow in the system. In this work, which is focused on the production quality paradigm in a model-based system engineering context, a digital prototype is proposed to integrate productivity and part quality based on the stream of variation analysis in multistage assembly systems. The prototype was modelled and simulated with OpenModelica tool exploiting the Modelica language capabilities for multidomain simulations and its synergy with SysML. A case study is presented to validate the potential applicability of the approach. The proposed model and the results show a promising potential for future developments aligned with the production quality paradigm. Full article

(This article belongs to the Special Issue Mechanical Tolerance Analysis in the Era of Industry 4.0)

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17 pages, 5160 KiB

Open AccessArticle

Analytical Model for Angular Distortion in Multilayer Welding under Constraints

by Woo-Jae Seong, Sang-Cheol Park and Hee-Keun Lee

Appl. Sci. 2020, 10(5), 1848; https://doi.org/10.3390/app10051848 - 7 Mar 2020

Cited by 1 | Viewed by 3516

Abstract

We propose an analytical model for the fast prediction of angular distortion that is caused by practical multilayer (or multi-pass) butt welding under constraints. To this end, the relationships between angular distortion, bead size, thickness, and degree of constraint are derived by analyzing [...] Read more.

We propose an analytical model for the fast prediction of angular distortion that is caused by practical multilayer (or multi-pass) butt welding under constraints. To this end, the relationships between angular distortion, bead size, thickness, and degree of constraint are derived by analyzing the welding deformation mechanism and considering the bead-on-plate welding experimental results. Prediction curves are then obtained while considering the geometry of the butt welding joint. We verify the formulas through experiments under various constraint conditions, with different welding joint geometries, heat inputs, and thicknesses. The proposed model can not only predict angular distortion in butt joints of various shapes, but also allows for providing restraint methods and welding sequences for minimizing distortion. Full article

(This article belongs to the Special Issue Mechanical Tolerance Analysis in the Era of Industry 4.0)

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