A Mathematical Model of the Assembly Error for Flat Surfaces

2021 ◽  
Author(s):  
Oleg V. Zakharov ◽  
K. G. Pugin ◽  
L. V. Seliverstova
Keyword(s):  
Mathematical Model ◽  
Flat Surfaces ◽  
Assembly Error

Mathematical Model of Flat Surface Machining Inaccuracies due to Elastic Strains of Technological System

2018 ◽  
pp. 1-14 ◽  
Author(s):  
I. I. Kravchenko
Keyword(s):  
Mathematical Model ◽  
Vector Field ◽  
Model Development ◽  
Technological System ◽  
Mutual Arrangement ◽  
Real Surface ◽  
Main Bearing ◽  
Flat Surfaces ◽  
Internal Surfaces ◽  
Elastic Strains

The paper considers the mathematical model development technique to build a vector field of the shape deviations when machining flat surfaces of shell parts on multi-operational machines under conditions of anisotropic rigidity in technological system (TS). The technological system has an anisotropic rigidity, as its elastic strains do not obey the accepted concepts, i.e. the rigidity towards the coordinate axes of the machine is the same, and they occur only towards the external force. The record shows that the diagrams of elastic strains of machine units are substantially different from the circumference. The issues to ensure the specified accuracy require that there should be mathematical models describing kinematic models and physical processes of mechanical machining under conditions of the specific TS. There are such models for external and internal surfaces of rotation [2,3], which are successfully implemented in practice. Flat surfaces (FS) of shell parts (SP) are both assembly and processing datum surfaces. Therefore, on them special stipulations are made regarding deviations of shape and mutual arrangement. The axes of the main bearing holes are coordinated with respect to them. The joints that ensure leak tightness and distributed load on the product part are closed on these surfaces. The paper deals with the analytical construction of the vector field F, which describes with appropriate approximation the real surface obtained as a result of modeling the process of machining flat surfaces (MFS) through face milling under conditions of anisotropic properties.

EXPERIMENTAL STUDY OF THE INFLUENCE OF THE MODE OF FINAL TREATMENT ON THE QUALITY OF THE FLAT SURFACES OF ALUMINIUM MATERIALS

2020 ◽  
pp. 30-35
Author(s):  
M. G. Galkin ◽  
A. S. Smagin ◽  
A. S. Poupyreva
Keyword(s):  
Mathematical Model ◽  
A Priori ◽  
Research Area ◽  
Machining Process ◽  
Second Phase ◽  
Forming Process ◽  
Flat Surfaces ◽  
Final Treatment ◽  
Priori Information

In the process of multivariate design of machining technology, one of the important tasks is to select the optimal cutting conditions at the final transitions of the forming process, providing a given quality of the surfaces on the workpiece made of the appropriate material. At the same time, to describe most of the design procedures of the machining process, there are problems associated with the algorithm for choosing the solution method, the response function and the range of acceptable solutions at all stages of processing. In this paper, as an algorithm for solving the problem, we propose the use of the known method of extreme planning of the experiment, which allows to obtain a mathematical model of the investigated multifactorial process with incomplete knowledge of its optimization mechanism. In the process of implementation of this algorithm in real production conditions on the basis of a priori information, the research area was chosen and the main levels of factors and intervals of their variation in this area were established. Then a full factorial experiment was carried out and its results were processed on the basis of a linear polynomial taking into account linear effects and interaction effects. As a result of testing the polynomial confidence intervals were determined for all regression coefficients by four parallel experiments at the same values of factors. In the second phase, were evaluated the adequacy of most mathematical models of the Fisher test. In the end, the transition from the coded values of the factors in the mathematical model to their natural values was carried out. Using the final model with natural values of the factors, a numerical experiment was conducted, which determined the optimum region with the most unfavorable treatment mode. Such a study allows to simplify the procedure for assigning the processing mode of the workpiece at the final stage in the conditions of the current production, while ensuring the specified quality of the machined surfaces and maintaining the productivity of the forming process. This technique is the subject of consideration in this work.

Analysis of the Transmission Error of Face-Gear Drives

1997 ◽  
Author(s):  
S. D. Chung ◽  
S. H. Chang ◽  
S. S. Lu
Keyword(s):  
Mathematical Model ◽  
Angular Displacement ◽  
Transmission Error ◽  
Contact Analysis ◽  
Generation Process ◽  
Face Gear ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Analytical Geometry ◽  
Assembly Error

Abstract Based on the face-gear generation process, the analytical geometry of face-gear drive with its mathematical model for tooth contact analysis of face-gear and spur pinion meshing was derived. In this paper, contact path and transmission error due to assembly misalignment were analyzed by using the proposed mathematical model and the tooth contact analysis. The effect of assembly error along the axis of face-gear, misalignment of crossed and angular displacement between axes of spur pinion and face-gear were all investigated. The results are illustrated by several examples.

HREM observation of dislocations near room temperature fractures in silicon

1988 ◽  
Vol 46 ◽  
pp. 892-893
Author(s):  
M. H. Rhee ◽  
W. A. Coghlan
Keyword(s):  
Cross Section ◽  
Room Temperature ◽  
Single Crystal Silicon ◽  
Dislocation Nucleation ◽  
Back Side ◽  
Ion Milling ◽  
Crystal Silicon ◽  
Flat Surfaces ◽  
Induced Fractures ◽  
Vicker’S Microhardness

Silicon is believed to be an almost perfectly brittle material with cleavage occurring on {111} planes. In such a material at room temperature cleavage is expected to occur prior to any dislocation nucleation. This behavior suggests that cleavage fracture may be used to produce usable flat surfaces. Attempts to show this have failed. Such fractures produced in semiconductor silicon tend to occur on planes of variable orientation resulting in surfaces with a poor surface finish. In order to learn more about the mechanisms involved in fracture of silicon we began a HREM study of hardness indent induced fractures in thin samples of oxidized silicon.Samples of single crystal silicon were oxidized in air for 100 hours at 1000°C. Two pieces of this material were glued together and 500 μm thick cross-section samples were cut from the combined piece. The cross-section samples were indented using a Vicker's microhardness tester to produce cracks. The cracks in the samples were preserved by thinning from the back side using a combination of mechanical grinding and ion milling.

A TEM study of electron tunneling in biological macromolecules

1987 ◽  
Vol 45 ◽  
pp. 140-141
Author(s):  
J. A. Panitz
Keyword(s):  
Stark Effect ◽  
Electron Tunneling ◽  
Imaging Modality ◽  
Tunneling Current ◽  
Biological Species ◽  
Scanning Tunneling ◽  
Biological Macromolecules ◽  
Flat Surfaces ◽  
Virus Particles ◽  
Stm Images

Tunneling is a ubiquitous phenomenon. Alpha particle disintegration, the Stark effect, superconductivity in thin films, field-emission, and field-ionization are examples of electron tunneling phenomena. In the scanning tunneling microscope (STM) electron tunneling is used as an imaging modality. STM images of flat surfaces show structure at the atomic level. However, STM images of large biological species deposited onto flat surfaces are disappointing. For example, unstained virus particles imaged in the STM do not resemble their TEM counterparts.It is not clear how an STM image of a biological species is formed. Most biological species are large compared to the nominal electrode separation of ∼ 1nm that is required for electron tunneling. To form an image of a biological species, the tunneling electrodes must be separated by a distance that would normally be too large for a tunneling current to be observed.

On the Faceting of Polar Ceramic Surfaces: Microscopy and Holography Studies of MGO(111) Surfaces

1996 ◽  
Vol 54 ◽  
pp. 366-367
Author(s):  
M. Gajdardziska-Josifovska ◽  
B. G. Frost ◽  
E. Völkl ◽  
L. F. Allard
Keyword(s):  
Electron Microscopy ◽  
High Vacuum ◽  
Ultra High Vacuum ◽  
Electron Holography ◽  
Flat Surfaces ◽  
Transmission Electron ◽  
Excess Surface ◽  
Polar Surfaces ◽  
Salt Structure ◽  
Crystallographic Planes

Polar surfaces are those crystallographic faces of ionically bonded solids which, when bulk terminated, have excess surface charge and a non-zero dipole moment perpendicular to the surface. In the case of crystals with a rock salt structure, {111} faces are the exemplary polar surfaces. It is commonly believed that such polar surfaces facet into neutral crystallographic planes to minimize their surface energy. This assumption is based on the seminal work of Henrich which has shown faceting of the MgO(111) surface into {100} planes giving rise to three sided pyramids that have been observed by scanning electron microscopy. These surfaces had been prepared by mechanical polishing and phosphoric acid etching, followed by Ar+ sputtering and 1400 K annealing in ultra-high vacuum (UHV). More recent reflection electron microscopy studies of MgO(111) surfaces, annealed in the presence of oxygen at higher temperatures, have revealed relatively flat surfaces stabilized by an oxygen rich reconstruction. In this work we employ a combination of optical microscopy, transmission electron microscopy, and electron holography to further study the issue of surface faceting.

Design of a Spectroscopic Low-Energy Emission Microscope

1990 ◽  
Vol 48 (1) ◽  
pp. 358-359
Author(s):  
Lee H. Veneklasen
Keyword(s):  
Parallel Imaging ◽  
Objective Lens ◽  
Energy Window ◽  
Flat Surfaces ◽  
Beam Voltage ◽  
New Instrument ◽  
Real Time Image ◽  
Image Planes ◽  
Backscatter Diffraction ◽  
Time Image

This paper discusses some of the unique aspects of a spectroscopic emission microscope now being tested in Clausthal. The instrument is designed for the direct parallel imaging of both elastic and inelastic electrons from flat surfaces. Elastic contrast modes of the familiar LEEM include large and small angle LEED, mirror microscopy, backscatter diffraction contrast (for imaging of surface structure), and phase contrast (for imaging of step dynamics)(1). Inelastic modes include topology sensitive secondary, and work function sensitive photoemission. Most important, the new instrument will also allow analytical imaging using characteristic Auger or soft X-ray emissions. The basic instrument has been described by Bauer and Telieps (2). This configuration has been redesigned to include an airlock, and a LaB6 gun, triple condensor lens, magnetic objective lens, a double focussing separator field, an imaging energy analyzer, and a real time image processor.Fig. 1 shows the new configuration. The basic beam voltage supply Vo = 20 KV, upon which separate supplies for the gun Vg, specimen Vs, lens electrode Vf, and analyzer bias Vb float. The incident energy at the sample can be varied from Vs = 0-1 KV for elastic imaging, or from Vg + Vs = (3 + Vs) KV for inelastic imaging. The image energy window Vs±V/2 may be varied without readjusting either the illumation, or imaging/analyzer optics. The diagram shows conjugate diffraction and image planes. The apertures defining incoming Humiliation and outgoing image angles are placed below the separator magnet to allow for their independent optimization. The instrument can illuminate and image 0.5-100 μm fields at 0-1 keV emission energies with an energy window down to 0.2 eV.

Mathematical model of hit phenomena and its application to movie advertisement

2008 ◽  
Author(s):  
Ishii Akira ◽  
Yoshida Narihiko ◽  
Hayashi Takafumi ◽  
Umemura Sanae ◽  
Nakagawa Takeshi
Keyword(s):  
Mathematical Model
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