A problem in the grinding with a small diametric wheel is the decrease of wheel speed. In order to resolve this problem, an accelerating unit which increases the wheel speed is recommended. In this paper, the accelerating effect of an accelerating unit has been investigated through the side-cut grinding experiments performed with a vitrified bonded CBN wheel in a machining center(MC). The static stiffness, normal force, and machining error were measured in the experiments. As the accelerating unit is attached on the column of machining center, the static stiffness of tool system is largely decreased. But as the wheel speed increased by the accelerating unit, this problem is overcome and machining efficiency is improved. The lesser the quill stiffness was, the higher the accelerating effect became.