Abstract
This paper reports the established conditions for static self-balancing for the case of an asymmetric rotor on two isotropic elastic supports, balanced by a passive automatic balancer of any type. In general, the plane of static imbalance does not coincide with the plane of an automatic balancer. The energy method has been used under the assumption that the mass of an automatic balancer's loads is much smaller than the mass of the rotor. It has been established that the static balancing of the rotor by an automatic balancer of any type is possible in the following cases: ‒ a long rotor when the rotor rotates at speeds between the first and second and above the third characteristic velocities; ‒ a spherical rotor when the rotor rotates at speeds between the first and second characteristic velocities; ‒ a short rotor at speeds exceeding a certain characteristic velocity provided that the automatic balancer is close to the center of the rotor mass. The rotor asymmetry increases the number of resonant speeds but the number of regions where the self-balancing is occurred does not change. The imbalance of the rotor and its location do not affect the characteristic rotation speeds of the rotor. An automatic balancer in the range of rotor rotation velocities that ensure the self-balancing tends to maximally reduce the deviation of its center from the rotor rotation axis. When the rotation velocity of a long or spherical rotor approaches the second characteristic speed, the automatic balancer's capacity ceases to provide for the complete elimination of the automatic balancer's axis deviation from the rotor's rotation axis. The result obtained summarizes the findings derived earlier when using the empirical criterion for the occurrence of self-balancing. The energy method, in contrast to the empirical method, has made it possible to estimate the residual deviation of the rotor's longitudinal axis from the rotation axis. That allows the estimation of the reserve or the calculation of the automatic balancer's balancing capacity. The type of automatic balancers is not taken into consideration in such studies. Therefore, the results obtained are suitable for automatic balancers of any type, and the method itself is suitable for constructing a general theory of passive self-balancing (applicable for automatic balancers of any type).
Highlights
Passive automatic balancers are used to balance fast-rotating rotors [1,2,3,4,5,6,7,8,9,10,11,12]
Our study suggests that an asymmetrical rotor that executes spatial motions and is mounted on two isotropic elastic supports can be statically balanced by a single automatic balancer of any type in the following case:
– a spherical rotor when the rotor rotates at velocities between the first and second characteristic speeds (42);
Summary
Passive automatic balancers are used to balance fast-rotating rotors [1,2,3,4,5,6,7,8,9,10,11,12]. The empirical [9] and energy [10] methods have been developed for this purpose The methods make it possible to answer the question on which conditions and over which range of rotation velocities can enable the balancing of a rigid or flexible, fixed in a certain way, rotor using one or more passive automatic balancers of any type. It is important to find the analytical conditions for establishing static self-balancing for an asymmetric rotor on two isotropic elastic supports for the case when the plane of the automatic balancer does not coincide with the plane of imbalance. This is the case most common in practice. On the other hand, resolving this issue is an important step in building the theory of a single-plane automatic balancing of rotors
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