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Shape Forming
Published in Christoph Gerhard, Optics Manufacturing, 2018
During grinding and lapping processes, the dimensions and the surface shape of plane and spherical optics surface are tested at regular intervals with the aid of so-called spherometers. In optical manufacturing, spherometers are also known as lensclocks, a special form of mechanical dial indicators. This measurement device usually features a resolution of ±50 μm and is used for controlling lens center thicknesses; the work piece thickness is compared to length standards or existing lens samples or prototypes. It is further employed for testing the surface shape (i.e., the deviation in actual radius of curvature from the target radius of curvature). The value measured in this case is the sagitta S (i.e., generally the height/depth of a circular arc). Since the lens clock is mounted on a spherometer ring (a.k.a. measuring bell), the sagitta results from the diameter Ds = 2 ∙ rs of this spherometer ring (given by its contact points on the lens surface) and the radius of curvature Rc of the lens surface as shown schematically in Figure 7.35.
Improving the Morrell C-model's accuracy in predicting the ball mills’ power draw based on calculating the dynamic voidage of grinding media
Published in Mineral Processing and Extractive Metallurgy, 2023
Mohammad Hasan Golpayegani, Bahram Rezai
First, based on the required ball size distribution and fractional mill filling, each ball size fraction’s weight was weighed and then charged to the glass-fronted ball mill. Then the rotating speed of the mill was adjusted using VFD. Once the load’s shape reached steady-state, the installed valve on the water pipeline was opened. Water was added until a circular segment with a measurable area appeared on the mill’s glass-fronted surface (see Figure 3). Then, the sagitta (height) of the circular segment (h) was measured by using an adjustable T-Square ruler (Figure 3). Finally, water was drained and weighed. To prevent water from being carried by the embedded lifters, 26 holes were made in each lifter’s body. The diameter of these holes was 2 mm, which was less than the diameter of the smallest balls (see Figure 2(c)).
Numerical simulations of the aerodynamic response of circular segments with different corner angles by means of 2D URANS. Impact of turbulence modeling approaches
Published in Engineering Applications of Computational Fluid Mechanics, 2018
M. Cid Montoya, F. Nieto, A. J. Álvarez, S. Hernández, J. Á. Jurado, R. Sánchez
Fundamental studies on the aerodynamic response of basic geometries such as circular cylinders (Choi, Jeon, & Kim, 2008; Sumner, 2010; Williamson, 1996; Zdravkovich, 1997, 2003; Zhang, Katsuchi, Zhou, Yamada, & Han, 2016) and rectangular cylinders (Bruno, Coste, & Fransos, 2012; Bruno, Salvetti, & Ricciardelli, 2014; Mariotti, Salvetti, Shoeibi Omrani, & Witteveen, 2016; Patruno, 2015; Ricci, Patruno, de Miranda, & Ubertini, 2016) have been a milestone in the foundation of the experimental fluid mechanics discipline, and more recently in the development of the computational approaches. Furthermore, these basic geometries can be recognized in the built environment such as in buildings or structural members (rectangular cylinders), as well as in power lines, stays in cable supported bridges, chimneys, mooring cables or high-rise buildings (circular cylinders). However, in recent years, new engineering problems in very different fields, and the introduction of certain non-conventional shapes in construction projects have demanded the analysis of different geometries, that have not been so extensively studied in the past. Circular segment geometries, whose geometry can be characterized by their corner angle β or the chord to sagitta ratio B/H (see Figure 1), are a good example of this statement.
Morphology of titanium coatings deposited through single pass cold spraying
Published in Materials and Manufacturing Processes, 2018
Umberto Prisco, Antonino Squillace, Antonello Astarita, Luigi Carrino
Once the best-fit circle has been assessed, its radius, r, as well as the central angle α and the area of the circular segment, which approximates the cross-sectional area of the deposited layer, can be expressed in terms of the chord B and the sagitta H, see Fig. 4. However, it is well known [16] that the following approximate formulas are valid when H << B as in the case under study: and