Treffer: Modification strategies for the top profile of algebraic spiral scroll compressors with equal-angle and unequal-angle approaches.

• Derived the formulas for the inner and outer wall profiles of the algebraic spiral. • Proposed two top profile modifications: equal-angle and unequal-angle types. • Designed eight modified top profiles with first-order continuous transitions. • Established a unified framework for algebraic spiral compressor top modification. To address the sharp-corner problem in the initial region of the algebraic spiral scroll profile, this study derives the mathematical expressions of the profile and the curvature radius formula, and provides geometric parameters for various modified profiles. On this basis, two categories of modification methods—equal-angle (EA) and unequal-angle (UA) modifications—comprising a total of eight specific methods are systematically proposed. Each category includes both symmetric and asymmetric geometric configurations. Methodologically, by constructing modification arcs and connection arcs in combination with the normal equidistant-offset principle, a natural transition and first-order tgeometric continuity in the initial region are achieved, significantly improving the smoothness of the profile's initial segment. In particular, the UA modification further enhances design flexibility by independently setting the starting modification angles and arc parameters for the inner and outer scroll walls. This research fills the theoretical gap in the modification modeling of algebraic spiral scroll compressor profiles and provides a comprehensive methodological framework and analytical models for profile optimization. [ABSTRACT FROM AUTHOR]