Based on a simple site-independent approach, we attempt to reproduce the solar $r$-process abundance with four nuclear mass models, and investigate the impact of the nuclear mass uncertainties on the $r$ process. In this paper, we first analyze the reliability of an adopted empirical formula for $beta$-decay half-lives which is a key ingredient for the $r$ process. Then we apply four different mass tables to study the $r$-process nucleosynthesis together with the calculated $beta$-decay half-lives, and the existing $beta$-decay data from FRDM+QRPA is also considered for comparison. The numerical results show that the main features of the solar $r$-process pattern and the locations of the abundance peaks can be reproduced well via the $r$-process simulations. Moreover, we also find that the mass uncertainties can significantly affect the derived astrophysical conditions for the $r$-process site, and resulting in a remarkable impact on the $r$ process.
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