  Using the stellar evolution code---Modules for Experiments in Stellar
Astrophysics (MESA), we investigate the evolution of massive stars with
different rotational velocities and metallicities towards Wolf-Rayet stars. In
our simulations, the initial rotating velocities are taken as 0, 250, 500 and
650 km s$^{-1}$, and the metallicities equal to 0.02, 0.014, 0.008, 0.006,
0.004 and 0.002. We show our rapid rotation models in the HR diagram compared
with the observations. We find that the rotational mixing is less efficient at
high metallicity, and these stars become Wolf-Rayet (WR) stars when the helium
in their center is ignited. However, rapid rotating massive stars at low
metallicity can easily evolve into WR stars due to the rotation resulted in
chemically homogeneous evolution. This can explain the origin of single WR
stars in galaxy at low metallicity. In our models, the observed SMC WR stars
are consistent with the single-star evolution models. However at higher
metallicities our single-star evolution models can only explain the luminous,
hydrogen-rich WN stars and O stars (which are classified as WR stars
previously).
