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Symmetry
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Axisymmetry in Mechanical Engineering
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Axisymmetry in Mechanical Engineering

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Engineering and Materials".

Deadline for manuscript submissions: closed (30 November 2022) | Viewed by 7955

Printed Edition Available!
A printed edition of this Special Issue is available here.

Special Issue Editor

Dr. Emanuel Willert

E-Mail Website
Guest Editor
Department of System Dynamics and Friction Physics, Institute of Applied Mechanics, Technische Universität Berlin, 10623 Berlin, Germany
Interests: contact mechanics; adhesion; friction; wear; materials science

Special Issue Information

Dear Colleagues,

Symmetry is an important concept in physics and engineering: What can be done with a system or an equation without changing it? Some might consider it aesthetically pleasing, while for others it is just an immensely useful property: one of the greatest “technologies” in human history is rolling, and anything that is supposed to roll has to have some kind of rotational symmetry. Symmetry simplifies calculations, both analytically and numerically. Accordingly, axisymmetric (or supposedly axisymmetric) systems are ubiquitous in engineering.

On the other hand, what is maybe even more interesting than symmetric systems are almost symmetric systems: Why is the symmetry broken or why is it still approximately retained?

The aim of the present Special Issue is thus to emphasize the phenomena of symmetry in mechanical engineering.

Dr. Emanuel Willert
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • symmetry and symmetry breaking in the physics of interfaces
  • symmetry in structural mechanics and fracture mechanics
  • axis symmetry in numerical methods in engineering
  • micro-contact models and mechanics of rough surfaces
  • contact mechanics and tribology of macroscopically axisymmetric systems
  • point excitation in engineering systems
  • applied problems focusing on the role of symmetry in mechanical engineering

Published Papers (7 papers)

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Editorial

Jump to: Research, Other

2 pages, 155 KiB  
Editorial
Guest Editorial: Special Issue “Axisymmetry in Mechanical Engineering”
by Emanuel Willert
Symmetry 2023, 15(1), 174; https://doi.org/10.3390/sym15010174 - 6 Jan 2023
Viewed by 856
Abstract
Axisymmetric (or almost axisymmetric) systems are ever-present in mechanical engineering [...] Full article
(This article belongs to the Special Issue Axisymmetry in Mechanical Engineering)

Research

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13 pages, 3429 KiB  
Article
Using Cylindrical and Spherical Symmetries in Numerical Simulations of Quasi-Infinite Mechanical Systems
by Alexander E. Filippov and Valentin L. Popov
Symmetry 2022, 14(8), 1557; https://doi.org/10.3390/sym14081557 - 28 Jul 2022
Cited by 1 | Viewed by 1548
Abstract
The application of cylindrical and spherical symmetries for numerical studies of many-body problems is presented. It is shown that periodic boundary conditions corresponding to formally cylindrical symmetry allow for reducing the problem of a huge number of interacting particles, minimizing the effect of [...] Read more.
The application of cylindrical and spherical symmetries for numerical studies of many-body problems is presented. It is shown that periodic boundary conditions corresponding to formally cylindrical symmetry allow for reducing the problem of a huge number of interacting particles, minimizing the effect of boundary conditions, and obtaining reasonably correct results from a practical point of view. A physically realizable cylindrical configuration is also studied. The advantages and disadvantages of symmetric realizations are discussed. Finally, spherical symmetry, which naturally realizes a three-dimensional system without boundaries on its two-dimensional surface, is studied. As an example, tectonic dynamics are considered, and interesting patterns resembling real ones are found. It is stressed that perturbations of the axis of planet rotation may be responsible for the formation of such patterns. Full article
(This article belongs to the Special Issue Axisymmetry in Mechanical Engineering)
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12 pages, 346 KiB  
Article
A Comparison of General Solutions to the Non-Axisymmetric Frictionless Contact Problem with a Circular Area of Contact: When the Symmetry Does Not Matter
by Ivan Argatov
Symmetry 2022, 14(6), 1083; https://doi.org/10.3390/sym14061083 - 25 May 2022
Cited by 6 | Viewed by 1673
Abstract
The non-axisymmetric problem of frictionless contact between an isotropic elastic half-space and a cylindrical punch with an arbitrarily shaped base is considered. The contact problem is formulated as a two-dimensional Fredholm integral equation of the first type in a fixed circular domain with [...] Read more.
The non-axisymmetric problem of frictionless contact between an isotropic elastic half-space and a cylindrical punch with an arbitrarily shaped base is considered. The contact problem is formulated as a two-dimensional Fredholm integral equation of the first type in a fixed circular domain with the right-hand side being representable in the form of a Fourier series. A number of general solutions of the contact problem, which were published in the literature, are discussed. Based on the Galin–Mossakovskii general solution, new formulas are derived for the particular value of the contact pressure at the contact center and the contact stress-intensity factor at the contour of the contact area. Since the named general solution does not employ the operation of differentiation of a double integral with respect to the coordinates that enter it as parameters, the form of the general solution derived by Mossakovskii as a generalization of Galin’s solution for the special case, when the contact pressure beneath the indenter is bounded, is recommended for use as the most simple closed-form general solution of the non-axisymmetric Boussinesq contact problem. Full article
(This article belongs to the Special Issue Axisymmetry in Mechanical Engineering)
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12 pages, 894 KiB  
Article
An Approximate Solution for the Contact Problem of Profiles Slightly Deviating from Axial Symmetry
by Valentin L. Popov
Symmetry 2022, 14(2), 390; https://doi.org/10.3390/sym14020390 - 15 Feb 2022
Cited by 8 | Viewed by 1937 | Correction
Abstract
An approximate solution for a contact problem of profiles which are not axially symmetrical but deviate only slightly from the axial symmetry is found in a closed explicit analytical form. The solution is based on Betti’s reciprocity theorem, first applied to contact problems [...] Read more.
An approximate solution for a contact problem of profiles which are not axially symmetrical but deviate only slightly from the axial symmetry is found in a closed explicit analytical form. The solution is based on Betti’s reciprocity theorem, first applied to contact problems by R.T. Shield in 1967, in connection with the extremal principle for the contact force found by J.R. Barber in 1974 and Fabrikant’s approximation (1986) for the pressure distribution under a flat punch with arbitrary cross-section. The general solution is validated by comparison with the Hertzian solution for the contact of ellipsoids with small eccentricity and with numerical solutions for conical shapes with polygonal cross-sections. The solution provides the dependencies of the force on the indentation, the size and the shape of the contact area as well as the pressure distribution in the contact area. The approach is illustrated by linear (conical) and quadratic profiles with arbitrary cross-sections as well as for “separable” shapes, which can be represented as a product of a power-law function of the radius with an arbitrary exponent and an arbitrary function of the polar angle. A generalization of the Method of Dimensionality Reduction to non-axisymmetric profiles is formulated. Full article
(This article belongs to the Special Issue Axisymmetry in Mechanical Engineering)
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26 pages, 6731 KiB  
Article
Coaxiality Optimization Analysis of Plastic Injection Molded Barrel of Bilateral Telecentric Lens
by Chao-Ming Lin and Yun-Ju Chen
Symmetry 2022, 14(2), 200; https://doi.org/10.3390/sym14020200 - 20 Jan 2022
Cited by 2 | Viewed by 1945
Abstract
Plastic optical components are light in weight, easy to manufacture, and amenable to mass production. However, plastic injection molded parts are liable to shrinkage and warpage as a result of the pressure and temperature variations induced during the molding process. Consequently, controlling the [...] Read more.
Plastic optical components are light in weight, easy to manufacture, and amenable to mass production. However, plastic injection molded parts are liable to shrinkage and warpage as a result of the pressure and temperature variations induced during the molding process. Consequently, controlling the process parameters in such a way as to minimize the geometric deformation of the molded part and improve the performance of the optical component as a result remains an important concern. The present study considered the problem of optimizing the injection molding parameters for the plastic lens barrel of a bilateral telecentric lens (BTL) containing four lens assemblies. The study commenced by using CODE V optical software to design the lens assemblies and determine their optimal positions within the barrel. Taguchi experiments based on Moldex3D simulations were then performed to determine the processing conditions (i.e., maximum injection pressure, maximum packing pressure, melt temperature, mold temperature, and cooling time) which minimize the coaxiality of the plastic barrel. Finally, CODE V and grayscale analyses were performed to confirm the optical performance of the optimized BTL. The Taguchi results show that the coaxiality of the plastic lens barrel is determined mainly by the maximum packing pressure and melt temperature. In addition, the CODE V and grayscale analysis results confirm that the optimized BTL yields a better modulus transfer function, spot diagram performance, and image quality than a BTL produced using the general injection molding parameters. Full article
(This article belongs to the Special Issue Axisymmetry in Mechanical Engineering)
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11 pages, 875 KiB  
Article
A Simple Semi-Analytic Contact Mechanical Model for Tangential and Torsional Fretting Wear of Axisymmetric Contacts
by Emanuel Willert
Symmetry 2021, 13(9), 1582; https://doi.org/10.3390/sym13091582 - 27 Aug 2021
Cited by 3 | Viewed by 1517
Abstract
Fretting wear of axisymmetric contacts is considered within the framework of the Hertz–Mindlin approximation and the Archard law for the linear wear. If the characteristic time scale for the wear is much larger than the duration of a single fretting oscillation, the profile [...] Read more.
Fretting wear of axisymmetric contacts is considered within the framework of the Hertz–Mindlin approximation and the Archard law for the linear wear. If the characteristic time scale for the wear is much larger than the duration of a single fretting oscillation, the profile change due to wear during one fretting cycle can be neglected for the contact problem as a zero-order approximation. This allows to give an exact contact solution during each fretting cycle, depending on the current worn profile, and thus for the explicit statement of an ordinary integro-differential equation system for the time-evolution of the fretting profile, which can be easily solved numerically. The proposed method gives the same results as a known, contact mechanically more rigorous simulation procedure that also operates within the framework of the Hertz–Mindlin approximation, but works significantly faster than the latter one. Tangential and torsional fretting wear are considered in detail. A comparison of the numerical prediction for the evolution of the worn profile in partial slip torsional fretting of a rubber ball on abrasive paper shows good agreement with experimental results from the literature. Full article
(This article belongs to the Special Issue Axisymmetry in Mechanical Engineering)
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Other

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1 pages, 191 KiB  
Correction
Correction: Popov, V.L. An Approximate Solution for the Contact Problem of Profiles Slightly Deviating from Axial Symmetry. Symmetry 2022, 14, 390
by Valentin L. Popov
Symmetry 2022, 14(10), 2108; https://doi.org/10.3390/sym14102108 - 11 Oct 2022
Cited by 3 | Viewed by 682
Abstract
There were misprints in Equations (40), (65), (66), and (67) in the original publication [...] Full article
(This article belongs to the Special Issue Axisymmetry in Mechanical Engineering)
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