22．已知点$A(x_{1}$，$y_{1})$，$B_{2}(x_{2}$，$y_{2})$，$C(x_{2}$，$0)$，$D(x_{1}$，$0)$，其中$x_{2}>0$，$x_{1}>0$，且${y}_{1}{x}_{1}^{2}-{x}_{1}+{y}_{1}=0$，${y}_{2}{x}_{2}^{2}-{x}_{2}+{y}_{2}=0$，若四边形$ABCD$是矩形，则此矩形绕$x$轴旋转一周得到的圆柱的体积的最大值为 ___$\frac{\pi }{4}$___．