ERROR PROCESSING METHOD OF CYCLOIDAL GEAR MEASUREMENT USING 3D COORDINATES MEASURING MACHINE

An error processing method is presented based on optimization theory and microcomputer technique which can be successfully used in the cycloidal gear measurement on three dimensional coordinates measuring machine (CMM). In the procedure, the minimum quadratic sum of the normal deviation is used as the object function and the equidistant curve is dealed with instead of the teeth profile. CMM is a high accurate measuring machine which can provide a way to evaluate the accuracy of the cycloidal gear completely.

ON DESIGN METHOD OF THE PRECISION CAM PROFILE WITH RANDOM PROCESSING ERRORS

Based on probability and statistic, a design method of precision cam profileconcerning the influence of random processing errors is advanced. Combining the design with theprocess, which can be used to predict that cam profiles will be successfully processed or not in thedesign stage, design of the cam can be done by balancing the economization and reliability. Inaddition, an fuzzy deduction method based on Bayers formula is advanced to estimate processingreasonable of the designed precision cam profile, and it take few samples.

Data processing and error analysis for the CE-1 Lunar microwave radiometer

The microwave radiometer （MRM） onboard the Chang＇ E-1 （CE-I） lu- nar orbiter is a 4-frequency microwave radiometer, and it is mainly used to obtain the brightness temperature （TB） of the lunar surface, from which the thickness, temperature, dielectric constant and other related properties of the lunar regolith can be derived. The working mode of the CE-1 MRM, the ground calibration （including the official calibration coefficients）, as well as the acquisition and processing of the raw data are introduced. Our data analysis shows that TB increases with increasing frequency, decreases towards the lunar poles and is significantly affected by solar illumination. Our analysis also reveals that the main uncertainty in TB comes from ground calibration.

A convenient look-up-table based method for the compensation of non-linear error in digital fringe projection

Although the structured light system that uses digital fringe projection has been widely implemented in three-dimensional surface profile measurement, the measurement system is susceptible to non-linear error. In this work, we propose a convenient look-up-table-based （LUT-based） method to compensate for the non-linear error in captured fringe patterns. Without extra calibration, this LUT-based method completely utilizes the captured fringe pattern by recording the full-field differences. Then, a phase compensation map is established to revise the measured phase. Experimental results demonstrate that this method works effectively.

ON THE CONVERGENCE PROBLEMS OF ISHIKAWA AND MANN ITERATIVE PROCESSES WITH ERROR FOR Φ-PSEUDO CONTRACTIVE TYPE MAPPINGS

The purpose of this paper is to introduce the concept of Φ_pseudo contractive type mapping and to study the convergence problem of Ishikawa and Mann iterative processes with error for this kind of mappings. The results presented in this paper improve and extend many authors'recent results.

ALGORITHM FOR SPHERICITY ERROR AND THE NUMBER OF MEASURED POINTS

The data processing technique and the method determining the optimal number of measured points are studied aiming at the sphericity error measured on a coordinate measurement machine （CMM）. The consummate criterion for the minimum zone of spherical surface is analyzed first, and then an approximation technique searching for the minimum sphericity error from the form data is studied. In order to obtain the minimum zone of spherical surface, the radial separation is reduced gradually by moving the center of the concentric spheres along certain directions with certain steps. Therefore the algorithm is precise and efficient. After the appropriate mathematical model for the approximation technique is created, a data processing program is developed accordingly. By processing the metrical data with the developed program, the spherical errors are evaluated when different numbers of measured points are taken from the same sample, and then the corresponding scatter diagram and fit curve for the sample are graphically represented. The optimal number of measured points is determined through regression analysis. Experiment shows that both the data processing technique and the method for determining the optimal number of measured points are effective. On average, the obtained sphericity error is 5.78 μm smaller than the least square solution, whose accuracy is increased by 8.63%; The obtained optimal number of measured points is half of the number usually measured.

Iterative Processes with Errors for Generalized Set-Valued φ-Hemi-contractive Mapping in Banach Spaces

A new conception of generalized set-valued Ф-hemi-contractive mapping in Banach spaces is presented. Some strong convergence theorems of Ishikawa and Mann iterative approximation with errors is proved. The results in this paper improve and extend the earlier results.

Iterative Approximation with Errors for Generalized Set-Valued Strongly Accretive Mapping in Banach Spaces

A new concept of generalized set-valued strongly accretive mappings in Banach spaces was given and some strong convergence theorems of Ishikawa and Mann iterative process with errors approximation methods by Huang et al. was proved. The results presented in this paper improve and extend the earlier results obtained by Huang et al.

Convergence Theorems of φ-pseudo Contractive Type Mappings in Normed Linear Spaces

In this paper, by virtue of an inequality and sane analysis techniques, we prove sane convergence theorems cm the iterative process for nonlinear mappings of-pseudo contractive type in named linear spaces, which extend and improve the corresponding results obtained by others recently.

Full-band error control and crack-free surface fabrication techniques for ultra-precision fly cutting of large-aperture KDP crystals

Large-aperture potassium dihydrogen phos- phate （KDP） crystals are widely used in the laser path of inertial confinement fusion （ICF） systems. The most common method of manufacturing half-meter KDP crystals is ultra-precision fly cutting. When processing KDP crystals by ultra-precision fly cutting, the dynamic characteristics of the fly cutting machine and fluctuations in the fly cutting environment are translated into surface errors at different spatial frequency bands. These machin- ing errors should be suppressed effectively to guarantee that KDP crystals meet the full-band machining accuracy specified in the evaluation index. In this study, the anisotropic machinability of KDP crystals and the causes of typical surface errors in ultra-precision fly cutting of the material are investigated. The structures of the fly cutting machine and existing processing parameters are optimized to improve the machined surface quality. The findings are theoretically and practically important in the development of high-energy laser systems in China.

An Implicit Iteration Process with Errors for a Finite Family of r-strictly Asymptotically Pseudocontractive Mappings

In this paper, we will establish several strong convergence theorems for the approximation of common fixed points of r-strictly asymptotically pseudocontractive mappings in uniformly convex Banach spaces using the modiied implicit iteration sequence with errors, and prove the necessary and sufficient conditions for the convergence of the sequence. Our results generalize, extend and improve the recent work, in this topic.

Machining Error Control by Integrating Multivariate Statistical Process Control and Stream of Variations Methodology

For aircraft manufacturing industries, the analyses and prediction of part machining error during machining process are very important to control and improve part machining quality. In order to effectively control machining error, the method of integrating multivariate statistical process control （MSPC） and stream of variations （SoV） is proposed. Firstly, machining error is modeled by multi-operation approaches for part machining process. SoV is adopted to establish the mathematic model of the relationship between the error of upstream operations and the error of downstream operations. Here error sources not only include the influence of upstream operations but also include many of other error sources. The standard model and the predicted model about SoV are built respectively by whether the operation is done or not to satisfy different requests during part machining process. Secondly, the method of one-step ahead forecast error （OSFE） is used to eliminate autocorrelativity of the sample data from the SoV model, and the T2 control chart in MSPC is built to realize machining error detection according to the data characteristics of the above error model, which can judge whether the operation is out of control or not. If it is, then feedback is sent to the operations. The error model is modified by adjusting the operation out of control, and continually it is used to monitor operations. Finally, a machining instance containing two operations demonstrates the effectiveness of the machining error control method presented in this paper.

Characterization of vortex structures with self-excited oscillations based on Liutex-Omega vortex identification method

The self-excited oscillation effect produces a continuous periodic pulsation without an external excitation source.It is widely used in fluid heat and mass transfer,cavitation and resistance reduction,and other related fields.The self-excited oscillation effect is significantly influenced by the vortex structure created by the jet passing through the specially designed cavity.The flow field in a self-excited oscillation cavity is simulated in this paper using the large eddy simulation(LES)method.The Liutex-Omega([Math Processing Error])method is used to analyze the vortex structure’s evolution inside the cavity and is contrasted with the Q-criterion,the λ_(2)-criterion,and the Omega(Ω)method.The studies indicate that the[Math Processing Error]method is less sensitive to threshold selection compared with other methods,while it is more capable of identifying weak vortices.The change in cavity vortex structure can be devided into the four stages of vortex ring priming,growth and development,wall touch separation,and fragmentation.The turbulent energy generated by shear effect can promote the growth and development of the vortex ring structure and has an important influence on the formation of the vortex ring structure.The vortex strength reveals the interaction mechanism between the shear effect and vortex rings.The vortex core area illustrates that the small-scale vortices are mainly distributed inside the collision walls of the cavity and the downstream flow channel.The Liutex-omega method has unique advantages in analyzing the cavity flow field and revealing the mechanism of self-excited oscillations.