Context. More and more evidence leads to considering classical Be stars as rotating close to the critical velocity. If so, then the question that arises is the origin of this high surface velocity. Aims. We determine which mechanisms accelerate the surface of single stars during the main sequence evolution. We study their dependence on the metallicity and derive the frequency of stars with different surface velocities in clusters of various ages and metallicities. Methods. We have computed 112 stellar models of four different initial masses between 3 and 60 Mʘ, at four different metallicities between 0 and 0.020, and with seven different values of the ratio Ω/Ωcrit between 0.1 and 0.99. For all the models, computations were performed until either the end of the main sequence evolution or until the critical limit was reached. Results. The evolution of surface velocities during the main sequence lifetime results from an interplay between meridional circulation (bringing angular momentum to the surface) and mass loss by stellar winds (removing it). The dependence on metallicity of these two mechanisms plays a key role in determining, for each metallicity, a limiting range of initial masses (spectral types) for stars able to reach or at least approach the critical limit. Present models predict a higher frequency of fast rotating stars in clusters with ages between 10 and 25 Myr. This is the range of ages where most of Be stars are observed. To reproduce the observed frequencies of Be stars, it is necessary to first assume that the Be star phenomenon already occurs for stars with υ/υcrit ≥ 0.7 and, second, that the fraction of fast rotators on the zero-age main sequence is higher at lower metallicities. Depending on the stage at which the star becomes a Be star, it may present either larger or less enrichments in nitrogen at the surface.