A study of the geometric design and gas port of the claw-type rotor

2009 ◽  
Vol 223 (9) ◽  
pp. 2063-2069 ◽  
Author(s):  
C-F Hsieh
Keyword(s):  
Mathematical Model ◽  
Geometric Design ◽  
Parameter Design ◽  
Simple Mathematical Model ◽  
Area Efficiency ◽  
Pumping Efficiency ◽  
Rotor Profiles

This article presents a simple mathematical model for the geometric design of a claw-type rotor. Based on the parameter design, the different claw shapes can be produced, and the design of gas ports and the fluid carryover will be discussed. Hence, a better design course will be proposed for the design of gas ports. Additionally, feasible design regions of the parameters are determined for avoiding the interference between two rotor profiles. Finally, the pumping efficiency will be estimated by the comparisons of carryover area and area efficiency in varied parameters designs. These results can indicate a better design course for the designer.

Towards a Theory of Experimentation for Expected Improvement

2005 ◽  
Author(s):  
Daniel D. Frey ◽  
Hungjen Wang
Keyword(s):  
Mathematical Model ◽  
Engineering Design ◽  
Parameter Design ◽  
Expected Improvement ◽  
Simple Mathematical Model ◽  
Adaptive Process ◽  
Design Alternatives ◽  
Factor Interactions ◽  
Main Effects

This paper concerns the role of experimentation in engineering design, especially the process of making improvements through parameter design. A simple mathematical model is proposed for studying experimentation including a model of adaptive one-factor-at-a-time experimentation. Theorems are proven concerning the expected value of the improvement provided by adaptive experimentation. Theorems are also proven regarding the probability that factor effects will be exploited by the process. The results suggest that adaptive one-factor-at-a-time plans tend to exploit two-factor interactions when they are large or otherwise exploit main effects if interactions are small. As a result, the adaptive process provides around 80% of the improvements achievable via parameter design while exploring a small fraction of the design alternatives (less than 20% if the system has more than five variables).

Geometric design of a pinion with two circularly arrayed conical teeth for roller drives

2006 ◽  
Vol 220 (9) ◽  
pp. 1405-1412 ◽  
Author(s):  
T-S Lai
Keyword(s):  
Mathematical Model ◽  
Coordinate Transformation ◽  
Geometric Design ◽  
Solid Modelling ◽  
Design Algorithm ◽  
Circular Arrays ◽  
Roller Drive ◽  
New Type ◽  
Design Case ◽  
Envelope Theory

This article presents a mathematical model and geometric design algorithm for a new type of roller drive. The pinion has conical teeth in two circular arrays instead of one. This work is based on coordinate transformation and envelope theory, from which the equation of meshing of the cycloid drive is derived. The pinion profiles are the equidistant curves of the epicycloid profiles except the contour of the pinion conical tooth holes. Although there are twice as many pinion teeth as conventional rollers, their speed ratios are identical. This approach can design roller drives in which the pinion has two circular arrays of conical and cylindrical rollers. On the basis of these results, the corresponding solid modelling is constructed by CAD. Four examples are presented to demonstrate the feasibility of this approach. These examples can be a useful reference as a design case for other tooth profiles.

scholarly journals A simple mathematical model that describes the growth of the area and the number of total and viable cells in yeast colonies

2014 ◽  
Vol 59 (6) ◽  
pp. 594-603 ◽  
Author(s):  
E.-M. Rivas ◽  
E. Gil de Prado ◽  
P. Wrent ◽  
M.-I. de Silóniz ◽  
P. Barreiro ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Simple Mathematical Model ◽  
Viable Cells
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