Multiple root resonance of tandem mill

The multiple-root resonance theory is introduced. The multiple-root resonance region is defined, and it includes the sub-multiple-root resonance region and complete-multiple-root resonance region. It is proved that the vibration mode shapes are identical if the natural frequencies are similar in size. The dynamic analysis of the 3-DOF model is investigated, and the results show that the variations of the mass ratio and stiffness ratio induce the natural frequencies approaching and forming a multiple-root resonance. The dynamic analysis of the tandem mill is made to study the multiple-root vibration, and the results show that with the increase in mass ratio, the 6th and 7th-order natural frequencies continue approaching one another and converge at the 5th-order natural frequency. The finite element analysis of the rolling mill shows that there are two similar natural frequencies in the rolling mill, and the vibration modes are not identical but have large vertical-component vibrations. The field test shows that the multiple-root resonance occurs in the tandem mill; after the foundation reconstruction, the multiple-root resonance is replaced by resonance with one dominant frequency, and the vibration is reduced.