In Pursuit of a Design Mathematics: Generalizing the Labeled Interval Calculus

Author(s):  
Walid Habib ◽  
Allen C. Ward

Abstract The Labeled Interval Calculus (LIC) is a formalism for reasoning about sets of design possibilities. Examples include toleranced objects, abstract descriptions involving many possible instantiations, and varying operating conditions. It has been successful in a “mechanical design compiler”, which accepts schematics and specifications and returns catalog numbers for optimal implementations. The LIC at present operates on monotonic algebraic equations and intervals of real values, but it now appears possible to generalize it to address arbitrary types of mathematical sets and relationships. The resulting family of formalisms is expected to be useful in design by feature and other design programs.

Author(s):  
Walid Habib ◽  
Allen C. Ward

Abstract The “labeled interval calculus” is a formal system that performs quantitative inferences about sets of artifacts under sets of operating conditions. It refines and extends the idea of interval constraint propagation, and has been used as the basis of a program called a “mechanical design compiler,” which provides the user with a “high level language” in which design problems for systems to be built of cataloged components can be quickly and easily formulated. The compiler then selects optimal combinations of catalog numbers. Previous work has tested the calculus empirically, but only parts of the calculus have been proven mathematically. This paper presents a new version of the calculus and shows how to extend the earlier proofs to prove the entire system. It formalizes the effects of toleranced manufacturing processes through the concept of a “selectable subset” of the artifacts under consideration. It demonstrates the utility of distinguishing between statements which are true for all artifacts under consideration, and statements which are merely true for some artifact in each selectable subset.


2021 ◽  
Author(s):  
Stefan D. Cich ◽  
J. Jeffrey Moore ◽  
Chris Kulhanek ◽  
Meera Day Towler ◽  
Jason Mortzheim

Abstract An enabling technology for a successful deployment of the sCO2 close-loop recompression Brayton cycle is the development of a compressor that can maintain high efficiency for a wide range of inlet conditions due to large variation in properties of CO2 operating near its dome. One solution is to develop an internal actuated variable Inlet Guide Vane (IGV) system that can maintain high efficiency in the main and re-compressor with varying inlet temperature. A compressor for this system has recently been manufactured and tested at various operating conditions to determine its compression efficiency. This compressor was developed with funding from the US DOE Apollo program and industry partners. This paper will focus on the design and testing of the main compressor operating near the CO2 dome. It will look at design challenges that went into some of the decisions for rotor and case construction and how that can affect the mechanical and aerodynamic performance of the compressor. This paper will also go into results from testing at the various operating conditions and how the change in density of CO2 affected rotordynamics and overall performance of the machine. Results will be compared to expected performance and how design changes were implanted to properly counter challenges during testing.


Author(s):  
W. John Calvert ◽  
Paul R. Emmerson ◽  
Jon M. Moore

Aircraft gas turbine engines require compression systems with high performance and low weight and cost. There is therefore a continuing drive to increase compressor stage pressure ratios, particularly for military fans. To meet this need, a technology acquisition programme has been carried out by QinetiQ and Rolls-Royce. Firstly, the stage matching issues for an advanced two-stage military fan were investigated, including the effects of employing variable inlet guide vanes. From this, the requirements for the first stage together with key operating conditions for the blading were defined. The blade profiles were then designed to satisfy the range of aerodynamic conditions using a quasi-3D calculation system. A satisfactory compromise between the aerodynamic and mechanical design requirements was reached in which a blisk construction was employed for the rotor, machined from a single piece of titanium. The new stage was manufactured and tested successfully, and it achieved its target flow, pressure ratio and efficiency on the first build. Detailed measurements of the internal flows using laser anemometry and high response pressure transducers were taken. Finally, these data have been analysed and used to calibrate current 3D multi-row CFD methods.


Author(s):  
O. Ancelet ◽  
S. Chapuliot

Ferritic steel 2 ¼ Cr is a candidate material for future pressure component in nuclear fields. In order to validate this choice, it is necessary, firstly to verify that it is able to withstand the planned environmental and operating conditions, and secondly to check if it is covered by the existing design codes, concerning its procurement, fabrication, welding, examination methods and mechanical design rules. A large R&D program on 2 ¼ Cr steel has been undertaken at CEA and Areva in order to characterize the behavior of this material and of its welded junctions. In this frame, a new measurement system for tensile testing was developed in the LISN laboratory of the CEA (French atomic commission), in order to characterize the local behavior of the material during a whole tensile testing. Indeed, with the conventional measurement system (typically an extensometer), the local behavior of the material can only be determinate during the stable step of the testing. So, usually the behavior of the material during the necking step of the step is unknown. This new measurement is based on the use of some laser micrometers which allow measuring the minimum diameter of the specimen and the curvature radius during the necking phase with a great precision. Thanks to the Bridgman formula, we can evaluate the local behavior of the material until the failure of the specimen. This new system was used to characterize the tensile propriety of a bimetallic welded junction of 2 ¼ Cr steel and austenitic stainless steel 316L(N) realized with inconel filler metal. These works lead to propose a tensile curve for each materials of the welded junction at room temperature and the effect of postweld heat treatment.


2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Tao He ◽  
Ning Ren ◽  
Dong Zhu ◽  
Jiaxu Wang

Efficiency and durability are among the top concerns in mechanical design to minimize environmental impact and conserve natural resources while fulfilling performance requirements. Today mechanical systems are more compact, lightweight, and transmit more power than ever before, which imposes great challenges to designers. Under the circumstances, some simplified analyses may no longer be satisfactory, and in-depth studies on mixed lubrication characteristics, taking into account the effects of 3D surface roughness and possible plastic deformation, are certainly needed. In this paper, the recently developed plasto-elastohydrodynamic lubrication (PEHL) model is employed, and numerous cases with both sinusoidal waviness and real machined roughness are analyzed. It is observed that plastic deformation may occur due to localized high pressure peaks caused by the rough surface asperity contacts, even though the external load is still considerably below the critical load determined at the onset of plastic deformation in the corresponding smooth surface contact. It is also found, based on a series of cases analyzed, that the roughness height, wavelength, material hardening property, and operating conditions may all have significant influences on the PEHL performance, subsurface von Mises stress field, residual stresses, and plastic strains. Generally, the presence of plastic deformation may significantly reduce some of the pressure spikes and peak values of subsurface stresses and make the load support more evenly distributed among all the rough surface asperities in contact.


Author(s):  
Yoriharu Murata ◽  
Naoki Shibukawa ◽  
Itaru Murakami ◽  
Joji Kaneko ◽  
Kenichi Okuno

The titanium 48-inch last stage blade that has world’s largest class exhaust annulus area and tip speed for 60Hz steam turbines has been developed. Concept of this blade is to achieve high performance and compact design of steam turbine for 1000MW thermal power plant and 300MW combined cycle plant. In the design of this blade, the optimization design has been done by using the recent analysis technologies, three dimensional CFD in aerodynamic design and FEA in mechanical design. The blade has curved axial fir-tree dovetail, snubber cover both at the tip and at the mid-span. To achieve superior vibration characteristics, continuously coupled structure was adopted for blade connection. To confirm the validity of design, first, sub-scale model blades were provided and tested in model steam turbine test facilities. Second, one row of actual size blades were assembled on the wheel of test rotor and were exposed rotating vibration test in a wheel box. Finally, these blades were tested at actual steam conditions in a full scale steam turbine test facility. In this paper, aerodynamic and mechanical design features will be introduced, and the test results of both sub-scale and actual size blades under real steam turbine operating conditions will be presented.


Author(s):  
O. Ancelet ◽  
G. Perez ◽  
L. Forest

Mod 9Cr-1Mo steel (T91) is a candidate material for steam generator of SFR (Sodium Fast Reactors). In order to validate this choice, it is necessary, firstly to verify that it is able to withstand the planned environmental and operating conditions, and secondly to check if it is covered by the existing design codes, concerning its procurement, fabrication, welding, examination methods and mechanical design rules. A large R&D program on mod 9Cr-1Mo steel has been undertaken at CEA in order to characterize the behavior of this material and of its welded junctions. In this frame, a new measurement system for tensile testing was developed in the laboratory of structural integrity and standards (LISN) of the CEA (French atomic commission), in order to characterize the local behavior of the material during a whole tensile testing. Indeed, with the conventional measurement system (typically an extensometer), the local behavior of the material can only be determined during the stable step of the testing. So, usually the behavior of the material during the necking step of the step is unknown. This new measurement is based on the use of some laser micrometers which allow measuring the minimum diameter of the specimen and the curvature radius during the necking phase with a great precision. Thanks to the Bridgman formula, we can evaluate the local behavior of the material until the failure of the specimen. This new system was used to characterize the tensile propriety of a bimetallic welded junction of Mod 9Cr-1Mo steel and austenitic stainless steel 316L(N) realized with GTAW process and inconel filler metal. These works lead to propose a tensile curve for each materials of the welded junction.


Author(s):  
Duccio Bonaiuti ◽  
Mehrdad Zangeneh

Optimization strategies have been used in recent years for the aerodynamic and mechanical design of turbomachine components. One crucial aspect in the use of such methodologies is the choice of the geometrical parameterization, which determines the complexity of the objective function to be optimized. In the present paper, an optimization strategy for the aerodynamic design of turbomachines is presented, where the blade parameterization is based on the use of a three-dimensional inverse design method. The blade geometry is described by means of aerodynamic parameters, like the blade loading, which are closely related to the aerodynamic performance to be optimized, thus leading to a simple shape of the optimization function. On the basis of this consideration, it is possible to use simple approximation functions for describing the correlations between the input design parameters and the performance ones. The Response Surface Methodology coupled with the Design of Experiments (DOE) technique was used for this purpose. CFD analyses were run to evaluate the configurations required by the DOE to generate the database. Optimization algorithms were then applied to the approximated functions in order to determine the optimal configuration or the set of optimal ones (Pareto front). The method was applied for the aerodynamic redesign of two different turbomachine components: a centrifugal compressor stage and a single-stage axial compressor. In both cases, both design and off-design operating conditions were analyzed and optimized.


1981 ◽  
Vol 103 (4) ◽  
pp. 731-738 ◽  
Author(s):  
C. C. Chamis ◽  
R. F. Lark ◽  
J. H. Sinclair

An investigation was conducted to determine the feasibility of superhybrid composite blades for meeting the mechanical design and impact resistance requirements of large fan blades for aircraft turbine engine applications. Two design concepts were evaluated: (1) leading edge spar (TiCom) and (2) center spar (TiCore), both with superhybrid composite shells. The investigation was both analytical and experimental. The results obtained show promise that superhybrid composites can be used to make light-weight, high-quality, large fan blades with good structural integrity. The blades tested successfully demonstrated their ability to meet steady-state operating conditions, overspeed, and small bird impact requirements.


Author(s):  
A. C. Ward ◽  
W. P. Seering

Abstract This paper introduces the theory underlying a computer program that takes as input a schematic of a mechanical or hydraulic power transmission system, plus specifications and a utility function, and returns catalog numbers from predefined catalogs for the optimal selection of components implementing the design. Unlike programs for designing single components or systems, this program provides the designer with a high level “language“ in which to compose new designs. It then performs much of the detailed design process. The process of “compilation”, or transformation from a high to a low level description, is based on a formalization of quantitative inferences about hierarchically organized sets of artifacts and operating conditions. This allows design compilation without the exhaustive enumeration of alternatives. The paper introduces the formalism, illustrating its use with examples. It then outlines some differences from previous work, and summarizes early tests and conclusions.


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