Methode zur stochastischen Optimierung von Schraubenrotorprofilen
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Date
2003-12-18
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Universität Dortmund
Abstract
The following thesis contributes to the broadening of the geometrical description ofrotor profiles for twin-screw compressors in dry operation by a spline-based descriptionand thus the connected new automatised possibilities. It leads to new possibilities ofgeometrical variations, which are more universal compared to classical methods ofprofile design. The development of an corresponding computer model is first carried outon the basis of generally applicable abstraction steps. Ensuing, exemplary optimisationsof single geometrical key figures of the profiles by evolutionary algorithms are used toasses the options and limitations of this method. An additional new aspect is, most ofall, to be found in the approach in form of a multiobjective optimisation, that is, thesimultaneous optimisation of several criteria without an initial determination ofcorresponding weights.This exposition begins with a functional abstraction to be able to heuristicallydetermine the relevance of physical and technical criteria concerning the operationalbehaviour by means of analysing their influence of a user s demands. From the resultthe importance of the geometrical parameters then is derived in a second step. Inconsequence an expected significant influence of the rotor profile on the operationalbehaviour becomes clear and constitutes the separation of the profile parameters ofadditional rotor data such as length and wrap angle. The following exposition thenconcentrates on the investigation of the subsystem, profile section.The large amount of flank parameters for the description of the profile require alimitation of the modelling to a low simulation depth with geometrical key figures,which can be calculated quickly. Consequently it abandons an exact thermodynamicsimulation at this stage, but the physical abstraction zooms on the definition of nondimensionalgeometrical key figures, which can be calculated from the rotor profile, andallow a comparison of different profile sections concerning the technical and physicalcriteria of the first step. These may be chosen and combined according to the givenoptimisation problem.The geometrical abstraction focuses on the comparison of analytical, discrete andspline-based formulations to describe the rotor profiles according to their handling, theirkey-figure ratings and the calculation of conjugated profiles within an automatedoptimisation process. Here the use of splines is to be favoured. Based on thisbackground bézier segments and b-splines form one rotor for the following optimisationfrom which the conjugated profile is calculated from the basic meshing conditions.Several exemplary optimisations of the profile section base on evolutionary algorithmsfor the variation of the flank form. Explicitly defined conditions for the validity of theflanks result in profiles with correct kinematics and with a closed contact line. First, aflank generator constructs a random profile, which is then optimised by mutation andrecombination steps with respect to simple geometric criteria. As a result, it is alwayspossible to successfully improve the starting profile with respect to the chosen keyfigure, on the one hand, whereas, on the other hand, there are some analytically provenextreme cases, which cannot be represented exactly. The reason for this shortcoming, ashas been proven by a geometrical analysis of the bézier segments, is the sensitivity ofthe basic meshing conditions on even slight errors of a flank s normal directions,especially concerning cycloids.Initially, investigations about different methods for weighing several criteriasimultaneously dominate the issue of multiobjective optimisations. On this backgroundthe term of Paretooptimal solutions is being discussed, by which no solution can beclearly favoured without applying weight. Here a product-based approach shows moresuperior results than the classical linear weighting.The example of the blowhole and the length of the contact line, which are both to beminimised, finally clearly demonstrates the formation of a Pareto-front whencontradictory criteria are being optimised, as well as the process of sifting the solutionsby applying a given weight. In principle, the geometrical restrictions remain the same asduring the optimisation of a single criterion, but the result is decidedly better.Future investigations should focus on the modification of the geometrical profiledescription in order to approximate analytical profile types more accurately. Also, afaster operation of the optimisation should be desirable. An extension of the method toattributes of the three-dimensional shape of the rotors will then permit the calculation ofmore exact key figures and provide an even more custom-designed rotor optimisationthan has been possible up to now.
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Keywords
Schraubenkompressor, Rotorprofil, Multi-kriterielle Optimierung, Paretofront, Gegenrotorberechnung, splines, twin-screw-compressor, rotor profile, multiobjective optimisation, pareto front, calculation of the conjugated profile, splines