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 ...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.展开更多
Purpose: The aim of this scientific contribution is to show the potential that integral calculus has offered to the analysis of thermodynamic processes. Method: Application of Integral Calculus. In this context, the d...Purpose: The aim of this scientific contribution is to show the potential that integral calculus has offered to the analysis of thermodynamic processes. Method: Application of Integral Calculus. In this context, the document covers the theoretical principles of integral calculus, such as Theoretical framework and background, Geometric interpretation of the primitive, Primitive existence theorem. Results: Integral calculus and generalized thermodynamic models, and their applications in various thermodynamic analysis contacts such as the Generalized Enthalpy Model, the Generalized Entropy Model, and the Generalized Model applied to gas mixtures and the General Model to elaborate the properties table. Conclusion: The mathematical analysis developed in this document is very useful in engineering and applied physics environments, a fact that supports its common pedagogical practice in university institutions.展开更多
基金This project is supported by National Natural Science Foundation of China (No.50475117)Municipal Science and Technology Commission of,Tianjin China(No.0431835116).
文摘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.
文摘Purpose: The aim of this scientific contribution is to show the potential that integral calculus has offered to the analysis of thermodynamic processes. Method: Application of Integral Calculus. In this context, the document covers the theoretical principles of integral calculus, such as Theoretical framework and background, Geometric interpretation of the primitive, Primitive existence theorem. Results: Integral calculus and generalized thermodynamic models, and their applications in various thermodynamic analysis contacts such as the Generalized Enthalpy Model, the Generalized Entropy Model, and the Generalized Model applied to gas mixtures and the General Model to elaborate the properties table. Conclusion: The mathematical analysis developed in this document is very useful in engineering and applied physics environments, a fact that supports its common pedagogical practice in university institutions.
