转子进动分析的4个定理

建立4个关于转子进动的定理.定理1为转子进动圆的面积定理;定理2为转子进动圆的周长定理;定理3和4则描述了转子上的作用力及其所作的功与转子进动的关系.应用上述定理,对不平衡力、阻尼力和反对称交叉刚度产生的弹性力所做的功进行了分析.所得结论与经典理论一致.但发现,ω_y＜Ω＜ω_x时,由于|r_-|＞r₊|,反对称交叉刚度产生的弹性力做负功,W＜0.这种情况下,反对称交叉刚度为镇定因素,有利于抑制反进动失稳. 

4 theorems on whirl transform of rotor vibration

The motion of a rotor can be decomposed into forward whirls and backward whirls. This approach is referred to as whirl analysis or whirl transform.It reveals the relationship between motion of a rotor and forces applied more evidently,therefore this method is widely applied to diagnosing problems in rotating machinery.4 theorems about rotation vibration were established.Theorem 1 states that,an elliptical orbit of a rotor can always be decomposed into a forward whirl and a backward whirl.The area of the elliptical orbit is equal to the absolute value of the difference between the area of the forward whirl and that of backward whirl.Theorem 2 is associated with the circumference of an elliptical orbit and its forward whirl and backward whirl.Theorem 3 states that,the forces applied to a rotor can also be decomposed into forward whirl force and backward whirl force.The forward whirl force can only perform work on the forward whirl but not on backward whirl;vice versa,the backward whirl force can only perform work on the backward whirl but does not on the forward whirl.Theorem 4 states that the work performed by forward whirl force is equal to the dot product of forward whirl force and the displacement of rotor in the forward whirl,similarly the work performed by backward whirl force is equal to the dot product of backward whirl force and the displacement of rotor in backward whirl.The theorems are applied to determine the work performed by unbalance,viscous damping and restoring forces due to skew symmetric stiffness.The results are identical with those obtained from traditional dynamics.However it is found that,when ω_y<Ω<ω_x,as |r_-|>|r₊|,the skew symmetric stiffness will act as a stabilizing force suppressing backward whirl of a rotor.