• Journal of Integrative Natural Science
• /
• v.7 no.2
• /
• pp.124-129
• /
• 2014

In this paper, we construct an logarithmic spiral-like curve using curvature-continuous quadratic spline and quadratic rational spline. The quadratic (rational) spline has self-similarity. We present some properties of the quadratic spline. Also using this $G^2$ quadratic spline, an approximation of logarithmic spiral is proposed and error analysis is obtained.

• Journal of the Korean Society for Precision Engineering
• /
• v.12 no.5
• /
• pp.46-56
• /
• 1995

As demands on the precision bevel gears are increased in the related industry, the exact kinematical investigations of a pair of spherical involute bevel gears are required for the computer aided design. The exact angular velocity ratio based on the characteristics of the spherical involute tooth is derived and verified from the relationship between rotational angles. Elementary kinematics of the gearsets is investigated by applying the transformation of the coordinate systems. The tooth contact lines based on logarithmic tooth-wise curve are examines in three dimentional space. Contact ratio is formulated and simulated according to the system parameters such as shaft angles, pressure angle, and spiral angles. The condition of teeth interference is dervied and the critical numbers of gear teeth are calculated. The whole surface geometry of a spiral bevel gearsets are discretized and visualized by a computer graphic tool.

• Journal of Industrial Technology
• /
• v.1
• /
• pp.39-45
• /
• 1981

The typical characteristic shape of the Koryo inlaid celadon Maebyong was reviewed and the symmetry of S curve was analyzed by the method of geometric basis. The contours of Maebyongs sampled were drawn and divided with geometric rectangular proportion. The analytical results showed the static and dynamic symmetric of the vase and the ratios of height and base of the rectangles established for the analysis of their shapes were almost 1:1, 1:${\sqrt{2}}$ and 3:5(known as the Golden Ratio). The excellent beauty of the curve was principally caused by the balanced and harmonius division of the proportional rectangles. The contour line was developed along with the logarithmic spiral modified and introduced lately into the shape of Yi dynasty's liquor bottle.

• Journal of computational fluids engineering
• /
• v.20 no.3
• /
• pp.35-40
• /
• 2015

Centrifugal pumps consume considerable amounts of energy in various industrial applications. Therefore, improving the efficiency of pumps machine is a crucial challenge in industrial world. This paper presents numerical investigation of flow characteristics in volutes of centrifugal pumps in order to compare the energy consumption. A wide range of volumetric flow rate has been investigated for each case. The standard k-${\varepsilon}$ is adopted as the turbulence model. The impeller rotation is simulated employing the Multi Reference Frames(MRF) method. First, two different conventional design methods, i.e., the constant angular momentum(CAM) and the constant mean velocity (CMV) are studied and compared to a baseline volute model. The CAM volute profile is a logarithmic spiral. The CMV volute profile shape is an Archimedes spiral curve. The modified volute models show lower head value than baseline volute model, but in case of efficiency graph, CAM curve has higher values than others. Finally for this part, CAM curve is selected to be used in the simulation of different cross-section shape. Two different types of cross-section are generated. One is a simple rectangular shape, and the other one is fan shape. In terms of different cross-section shape, simple rectangular geometry generated higher head and efficiency. Overall, simulation results showed that the volute designed using constant angular momentum(CAM) method has higher characteristic performances than one by CMV volute.

• The KSFM Journal of Fluid Machinery
• /
• v.13 no.2
• /
• pp.59-64
• /
• 2010

A design method of Sirocco fan is developed for constructing 3-D impeller and scroll geometries, and for predicting both the aerodynamic performance and the noise characteristics of the designed fan. The aerodynamic blading design of fan is conducted by blade angle, camber line determinations and airfoil thickness distribution, and then the scroll geometry of fan is designed by using logarithmic spiral. The aerodynamic performance of designed fan is predicted by the meanline analysis with flow blockage, slip and pressure loss correlations. Based on the predicted performance data, fan noise is predicted by two models for cutoff frequency and broadband noise sources. The present predictions for the performance and the noise level of actual fans are well agreed with measurement results.

• Geotechnical Engineering
• /
• v.10 no.2
• /
• pp.121-140
• /
• 1994

This paper presents the probabilistic model to evaluate the three-dimensional stability of layered deposits and c-0 soil slopes. Rotational slides are assumed with a cylindroid control part terminated with plane ends. And the potential failure surfaces in this study are assumed with the logarithmic spiral curve refracted at boundary of layers. This model takes into consideration the spatial variabilities of soil properties and the uncertainties stemming from insufficient number of samples and the discrepancies between laboratory measured and in -situ values of shear strength parameters. From the probabilistic approxi mate method (FOSM and SOSM method), the mean and variance of safety factor are calculated, respectively. And the programs based on above models is developed and a case study is analysed in detail to study the sensitivity of results to variations in different parameters by using the programs developed in this study. On the basis of thin study the following conclusions could be stated : (1) The sensitivity analysis shown that the probability of failure is more sensitive to the uncertainty of the angle of internal friction than that of the cohesion, (2) The total 3-D proability of failure and the critical width of failure are significantly affected by total width of slope. It is found that the total 3-D probability of failure and the critical width of failure increase with increasing the slope width when seismic forces do not exist and the total 3-D probability of failure increases with increasing the slope width and the critical width of failure decreases when seismic intensity is relatively large, (3) A decrease in the safety factor (due to effect such as a rise in the mean ground water level, lower shear strength parameters, lower values for the correction factors, etc.) would result in reduction in the critical width of failure.