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| Abastract：By specifying not parameterizations of the curve, but instead the radius of curvature as a function of tangent direction and using the intrinsic equation of a planar curve, the design can be changed in a way that allows all relevant geometrical quantities to be calculated in closed analytical form. Aiming at scroll profiles, summarization on scroll profile engagement theory, conjugate profile pitch line theory, general control equation and general equation were studied. The geometry equation of stroke volume, inner volume ratio, length of profile and radius of curvature etc. were carried out. Summarization on general scroll profile, conjugate profile pitch line and its control equation were given. The shortage of general scroll profile in existence and the theoretic one sidedness of control equation were analyzed. A new methodology based on functional theory to study scroll profile that widening method for general profile design of scroll compressor was developed. Using functional analysis theory, general functional equation that can represent random geometry and integrate all mathematical models of scroll profile in exiting was established. It offers an opportunity for studying scroll profile theory adopting functional theory and analyzing scroll profile in different ranks metric space. |
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| Keywords:Scroll compressor, scroll profiles, summarization, geometry theory |
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