Vibration Control of Shafts via Automatic Passive Balancing

Open Access
Author:
Haidar, Ahmad M
Graduate Program:
Aerospace Engineering
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
July 05, 2018
Committee Members:
  • Jose Palacios, Dissertation Advisor
  • Jose Palacios, Committee Chair
  • George A Lesieutre, Committee Member
  • Edward Smith, Committee Member
  • Christopher Rahn, Outside Member
  • Namiko Yamamoto, Committee Member
Keywords:
  • structural dynamics
  • vibration control
  • rotordynamics
  • aerospace engineering
  • automatic passive balancing
Abstract:
A physics-based model of a rotary system is derived and proposed with several advancements in passive balancer modeling. The model was used to study the performance and dynamic behavior of passive balancing devices. Through experiment, it was verified for conventional and partitioned ball-type passive balancers. A passive balancer consists of masses that are free to move along a race that is concentric with a shaft axis of rotation. Beyond the first flexural critical speed of a shaft, the bending response lags 180 degrees relative to the imbalance phase causing the masses to assume positions that counter imbalance and reduce vibration. Passive balancing reliably and significantly reduces imbalance vibrations in supercritical operation. Comprehensive modeling is required to capture this nonlinear phenomenon. The research outlined in this dissertation targets several shortcomings in the state-of-the-art of passive balancing. First, conventional balancers cause an increase in vibration compared to a system without a balancer during critical speed transitions. Previous experimental work, limited to supercritical operation, demonstrated benefits of partitioned-track balancers such as forced synchronization. No model, however, exists for predicting and optimizing performance with partitions. Models in literature do not consider friction due to ball-ball contact and ball slipping. It is shown in this work that those must be considered to predict the balancer response when the track lacks viscous damping. Finally, there is no consideration of centrifugal clamps in literature neither analytically nor experimentally. The potential vibration reduction using centrifugal clamps is demonstrated in this research. The model developed here is capable of predicting the balancing response. It is a model of a flexible rotary system with imbalance, gravity, rotational inertia, and variable shaft speed. Advancements in balancer modeling include new designs and friction dynamics. Equations of motion of a centrifugally clamped passive balancer are provided. A multi-body collision detection algorithm allows for tracks to be configured with partitions and handles multi-ball collisions. Damping due to drag was considered with Reynolds number dependence. The friction model includes the effects of resistance due to both ball-ball and ball-track contact. The model does not limit the ball motion to rolling as done in models found in literature. Balancer ball slipping, rolling, and rotational inertia are considered. Parametric studies were conducted to determine the impact of key parameters on vibration control performance, and the tuning prospects of each parameter are determined. For the coefficients of restitution, it was shown the parameter had negligible impact (<10% deviation) on performance in the tested configurations. The balancer location relative to the source of imbalance proved to be critical with peak performance being in proximity of the imbalance. Results for balancer configuration parameters such as number of tracks, balls and partitions indicated varying ball mass had no impact on mitigating the effect of rolling resistance. Increasing the track radius degraded performance -- 39% more vibration in the 3-track balancer compared to the 1-track. Increasing the number of partitions improved performance in all operating conditions. It was shown analytically that the partitioned passive balancer (PPB) partitions force a synchronization of the balancing masses even with a lack of viscous damping in the track. The rolling resistance parametric study confirmed optimal performance at low resistance. It was also found that the non-partitioned passive balancer (PB) had a higher tolerance for increased rolling resistance maintaining performance better than the PPB configuration. It was demonstrated that the shaft acceleration rate can be tuned in the PPB configuration to match vibration of the non-balanced system during critical speed transitions. Finally, it was determined that if the centrifugal clamp release speed exceeds the shaft critical speed, the passive balancer can effectively reduce vibration during critical speed transitions (up to 95% reduction demonstrated). Experiments were conducted on the PSU Tailrotor Driveshaft, a supercritical, frequency-scaled helicopter tailrotor test rig. Characteristics of the test rig and methodologies for measuring parameters such as the coefficients of restitution and rolling resistance are provided. Experimental results demonstrate that a partitioned passive balancer is superior to a non-partitioned conventional balancer. During shaft speed up, the PPB configuration reduced vibration due to imbalance by 5% on average. At supercritical steadystate, it reduced vibration by 62%, and at speed down, it reduced vibration by 51%. The PPB configuration performed better than the PB configuration in all conditions -- the latter causing an increase in vibration in many cases. The PPB configuration was 83% efficient in using its mass for counter-balancing at supercritical operation. The proposed model accurately predicted shaft vibration amplitudes within 14% at supercritical operation across all tested balancing configurations. Including predictions of peak vibration amplitudes in critical speed transitions, the model predictions were within 35% of all experimental values.