Based on the two-dimensional model, the formation mechanism of quantum vortex by the expansions and superpositions of the many sub-Bose-Einstein condensations (BECs) in the weak harmonic trap is studied. In the harmonic approximation, the initial wave function of the sub-BEC is Gaussian function. Once the initial wave function is known, by using the propagation method, the time evolution of the wave function for the sub-BECs could be obtained. The physical processes of the macroscopic quantum vortex formed by the symmetric distribution of the three sub-BEC expansions and superpositions are analyzed, and the law of quantum vortex with time evolution is obtained. It is found that the vortex distribution is oscillatory in the harmonic trap, and vortex and anti-vortex are mutually transformed in time. At the same time of evolution, the vortex direction is always opposite to that of the neighbor vortex, and at different evolutionary times t and t', which satisfy a relation of t+t'=T (period of harmonic trap), the position of vortex nucleus is unchanged, but the vortex is transformed into the anti-vortex. These basic phenomena of quantum vortex are explained and discussed. In particular, in this paper we also introduce the particle flow density, calculate the flow circulation of our system, and analyze the mechanism of vortex formation. The research ideas and methods in this paper are easily to be extended to the study about the vortex formed by more than three sub-BEC expansions and superpositions, and they can also be used to discuss the effects of sub-BECs with different initial phase differences. This model is also easier to implement in experiment. Therefore, the research of this paper also has enlightenment to the experimental work.