Application of Zernike polynomials to test large aspheric surfaces in the fine grinding stage

2010 ◽  
Author(s):  
Yangfang Deng ◽  
Jianguan Tang ◽  
Fan Wu
Keyword(s):  
Zernike Polynomials ◽  
Aspheric Surfaces ◽  
Fine Grinding

Tilt angle correction based forming algorithm for high steepness aspheric surfaces polishing

Optik ◽  
2021 ◽  
pp. 167082
Author(s):  
Changjun Jiao ◽  
Yong Shu ◽  
Zhen Zhang ◽  
Bo Wang ◽  
Feihai Gao
Keyword(s):  
Tilt Angle ◽  
Aspheric Surfaces ◽  
Angle Correction

scholarly journals Potentials of Vitrified and Elastic Bonded Fine Grinding Worms in Continuous Generating Gear Grinding

2021 ◽  
Vol 5 (1) ◽  
pp. 4
Author(s):  
Maximilian Schrank ◽  
Jens Brimmers ◽  
Thomas Bergs
Keyword(s):  
High Performance ◽  
Manufacturing Processes ◽  
Fine Grinding ◽  
Gear Grinding ◽  
Profile Line ◽  
Grinding Tool ◽  
Process Behavior ◽  
Hard Finishing ◽  
Tooth Flank ◽  
Process Strategy

Continuous generating gear grinding with vitrified grinding worms is an established process for the hard finishing of gears for high-performance transmissions. Due to the increasing requirements for gears in terms of power density, the required surface roughness is continuously decreasing. In order to meet the required tooth flank roughness, common manufacturing processes are polish grinding with elastic bonded grinding tools and fine grinding with vitrified grinding tools. The process behavior and potential of the different bonds for producing super fine surfaces in generating gear grinding have not been sufficiently scientifically investigated yet. Therefore, the objective of this report is to evaluate these potentials. Part of the investigations are the generating gear grinding process with elastic bonded, as well as vitrified grinding worms with comparable grit sizes. The potential of the different tool specifications is empirically investigated independent of the grain size, focusing on the influence of the bond. One result of the investigations was that the tooth flank roughness could be reduced to nearly the same values with the polish and the fine grinding tool. Furthermore, a dependence of the roughness on the selected grinding parameters could not be determined. However, it was found out that the profile line after polish grinding is significantly dependent on the process strategy used.

On the circle polynomials of Zernike and related orthogonal sets

1954 ◽  
Vol 50 (1) ◽  
pp. 40-48 ◽  
Author(s):  
A. B. Bhatia ◽  
E. Wolf
Keyword(s):  
Unit Circle ◽  
Generating Functions ◽  
Legendre Polynomials ◽  
Phase Contrast ◽  
Diffraction Theory ◽  
Zernike Polynomials ◽  
Optical Aberrations ◽  
Orthogonal Set ◽  
Complete Orthogonal Set ◽  
Explicit Expressions

ABSTRACTThe paper is concerned with the construction of polynomials in two variables, which form a complete orthogonal set for the interior of the unit circle and which are ‘invariant in form’ with respect to rotations of axes about the origin of coordinates. It is found that though there exist an infinity of such sets there is only one set which in addition has certain simple properties strictly analogous to that of Legendre polynomials. This set is found to be identical with the set of the circle polynomials of Zernike which play an important part in the theory of phase contrast and in the Nijboer-Zernike diffraction theory of optical aberrations.The results make it possible to derive explicit expressions for the Zernike polynomials in a simple, systematic manner. The method employed may also be used to derive other orthogonal sets. One new set is investigated, and the generating functions for this set and for the Zernike polynomials are also given.

Effects of Two-Step DC Electrochemical Pretreatment of Fine Grinding WC-Co Tool Surface on Morphology and Quality of Diamond Coatings

2011 ◽  
Vol 337 ◽  
pp. 59-62
Author(s):  
Xiang Hui Zhang ◽  
Ling Wang ◽  
Jian Ping Long
Keyword(s):  
Surface Morphology ◽  
Direct Current ◽  
Arc Discharge ◽  
Etching Time ◽  
Diamond Coating ◽  
Diamond Coatings ◽  
Fine Grinding ◽  
Electrolytic Etching ◽  
Electrochemical Pretreatment

In the present investigation, diamond coating was deposited on fine grinding cemented carbide substrate by direct current arc discharge chemical vapor deposition. The effect of electrolytic etching time in the two-step electrochemical pretreatment process (firstly using electrolytic etching, and then using acid etching) on morphology and quality of the diamond coating were systemically studied. The surface morphology feature and quality of diamond coatings were characterized by means of Scanning Electron Microscope (SEM), laser Raman spectrometer respectively. The results showed that the electrolytic etching duration has distinctly effect on the quality and crystal features such as morphology, crystal type and grain size of diamond coating. It showed that as electrolytic current is direct current 3A, electrolytic etching time altering from 0.5 min to 7.5min, the surface morphology of diamond films gradually transition from microcrystalline cubic-octahedron to cauliflower type nanocluster, and further increase the electrolytic etching time, will lead to several negative effects on the quality and nucleation of the coatings which is not only retard the diamond nucleation, but also promote the formation of graphite.

scholarly journals Optical Design of the Goaly3 Multi-Mirror Telescope System with a Wide Field of View

2021 ◽  
Vol 11 (3) ◽  
pp. 1200
Author(s):  
Junliu Fan ◽  
Quanying Wu ◽  
Baohua Chen ◽  
Lin Liu ◽  
Lei Chen
Keyword(s):  
Fill Factor ◽  
Optical Design ◽  
Tolerance Analysis ◽  
Field Of View ◽  
Wide Field ◽  
Aspheric Surfaces ◽  
The Monte Carlo Method ◽  
Wide Field Of View ◽  
Mirror Telescope ◽  
Telescope System

A Golay3 multi-mirror telescope (MMT) system is designed in this paper. The fill factor of the Golay3 MMT is derived from the angular resolution of the telescope. An initial configuration is established according to the paraxial optical theory. A three-element aspheric corrector group is designed and placed in the converging light cone to enlarge the field of view (FOV) of the Golay3 MMT. The tolerance analysis for each surface of the Golay3 MMT is conducted using the Monte Carlo method. The design results show the FOV of the Golay3 MMT system can be increased to 1.5° with the insertion of a three-element aspheric corrector group. The results of the tolerance analysis indicate that most tolerances are loose, while some decenter tolerances relating with the aspheric surfaces are relatively tight, but still within an acceptable range.

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