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As a geometric property that cannot overlap with its mirror image, chirality is becoming more and more common in electronic structures. The recent discovery of chiral topological polar structures in artificial ferroelectric superlattices is not only of scientific importance but also holds promise for application in tunable frequency oscillators. Although the tubular chiral polarization vortex has been observed in PbTiO3/SrTiO3 superlattices, the conditions for its stability remain elusive. Here, we construct a temperature-strain phase diagram for the (PbTiO3)10/(SrTiO3)10 superlattices by using phase field simulation in which four domain states exist at different temperatures and misfit strains. It is found that the chiral polarization vortex appears only in a small range of misfit strain, elucidating the absence of chirality in most ferroelectric superlattices. The chiral polarization vortex is an intermediate state between the ordinary achiral polarization vortex and the mixed domain structure. In addition, by changing strain or temperature, chiral vortices can be reversibly transformed into achiral vortices, demonstrating its tunability. The present work provides theoretical guidance for creating the chiral vortex in ferroelectric superlattices. [ABSTRACT FROM AUTHOR]