axial vibration
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The axial vibration of a shaft-bearing system induced by the thrust excitation is usually composed of multiple tones. To suppress the axial vibration of the shaft-bearing system, two inertial electro-magnetic actuators are mounted symmetrically at the thrust bearing and work in parallel to exert control forces. The control signal is generated by an adaptive algorithm with subband filtering, which aims to attenuate over a broadband the vibration of the thrust bearing and its foundation induced by the dynamic thrust force. To reduce computational complexity, the recursive computation is partly realized with the auto-regressive moving average (ARMA) model. The proposed active control approach is evaluated numerically at first with the dynamic model of the shaft-bearing system and then verified with an experimental system. It is demonstrated by the numerical and experimental results that the active control approach is able to suppress the multi-tone vibration of the thrust bearing and the foundation. Moreover, in comparison to the single-band adaptive feedback algorithm, the adaptive algorithm with subband filtering is more effective when the disturbance contains multiple tones.

Abstract The rotor misalignment fault, which occurs only second to unbalance, easily occurs in the practical rotating machinery system. Rotor misalignment can be further divided into coupling misalignment and bearing misalignment. However, most of the existing references only analyze the effect of coupling misalignment on the dynamic characteristics of the rotor system, and ignore the change of bearing excitation caused by misalignment. Based on the above limitations, a five degrees of freedom nonlinear restoring force mathematical model is proposed, considering misalignment of bearing rings and clearance of cage pockets. The finite element model of the rotor is established based on the Timoshenko beam element theory. The coupling misalignment excitation force and rotor unbalance force are introduced. Finally, the dynamic model of the ball bearing-coupling-rotor system is established. The radial and axial vibration responses of the system under misalignment fault are analyzed by simulation. The results show that the bearing misalignment significantly influences the dynamic characteristics of the system in the low-speed range, so bearing misalignment should not be ignored in modeling. With the increase of rotating speed, rotor unbalance and coupling misalignment have a greater impact. Misalignment causes periodic changes in bearing contact angle, radial clearance, and ball rotational speed. It also leads to reciprocating impact and collision between the ball and cage. In addition, misalignment increases the critical speed and the axial vibration of the system. The results can provide a basis for health monitoring and misalignment fault diagnosis of the rolling bearing-rotor system.

A circulating water pump is a key equipment of cooling systems in nuclear power plants. Several anchor bolts were broken at the inlet rings of the same type of pumps. The bolts were turned by a special material for seawater corrosion protection. There were obvious turning tool marks at the root of the thread, which was considered as the source of the crack. The fatigue crack extended to the depth of the bolt, causing obvious radiation stripes on the fracture surface, which was a typical fatigue fracture. Obvious overtightening characteristics were found at the head of the broken bolt. Fracture and energy spectrum analysis showed that the bolt was not corroded. The axial vibration of the pump was measured. The static tensile stress along the bolt axis caused by the preload, the axial tensile stress caused by the axial vibration, and the torsional stress were calculated, respectively. According to the fatigue strength theory, the composite safety factor of the bolt fatigue strength was 1.37 when overtightening at 1.2 times the design torque, which was less than the allowable safety factor of 1.5-1.8, so the bolt was not safe, which further verified the conclusion of fracture analysis. The reason for the low safety factor was caused by the overtightening force. The improvement method was to control the bolt preload or increasing the bolt diameter.

Abstract Studies show that the applied torque and load on the worktable of a dual-turntable five-axis machine tool continuously changes during the machining process. These variations generate vibration in the worktable along the axial direction, thereby reducing the machining accuracy. In order to improve the machining accuracy of the machine tool and the dynamic characteristics of the worktable, this paper first established the nonlinear dynamic equation of the axial vibration of the machine tool table when the worktable is subjected to torque, swing moment and load according to the elasticity of the plate and shell; then according to Galerkin The truncation method solves the dynamic displacement in the axial direction of the worktable, as well as the bifurcation diagram, displacement waveform diagram, phase plane trajectory and Poincaré cross-section diagram of the processing system; Finally, the influence of different parameters, including torque, swing moment, and load on axial vibration of the worktable was analyzed during the tool operation. The obtained results reveal that as the external load changes, the corresponding axial vibration of the worktable is mainly in the state of large periodic motion, where the maximum vibration amplitude reaches 0.09mm, and the external load has the greatest influence on the axial vibration of the worktable. Moreover, the axial vibration of the worktable is affected by the swing moment. More specifically, in the chaotic state of a small period and small area, the maximum vibration amplitude reaches 0.03mm, and the swing moment has a negligible effect on the axial vibration of the worktable. The influence of torque and load on the vibration characteristics of the five-axis machine tool table during machining was studied through experiments. The obtained results demonstrate that non-linear analysis of the table axial vibration of the five-axis machine tool with dual turntables is an effective way to control the stability of the worktable during the processing of the workpiece.

In this paper, a nine degree-of-freedom dynamic model of the ball screw feed system considering the contact nonlinearity between balls and raceways is established to analyze the vibration characteristics. The position relationship between raceway centers for the ball screw and bearings is determined by using the homogeneous coordinate transformation, and then the restoring force functions along the axial and lateral directions are derived. The dynamic equations of the feed system are solved by using Newmark method, and the proposed model is verified by the experimental method. Furthermore, the effect of the excitation amplitude on the axial vibration of the feed system is investigated by the frequency-amplitude curve and 3-D frequency spectrum. With the increase of excitation amplitude, the dynamic response of the feed system exits the softening, hardening type nonlinearity and jump phenomenon. Additionally, the effects of the initial contact angle, length of screw shaft and number of loaded balls on the axial vibration of the feed system in the resonance region are discussed. The results show that the dynamic model established in this paper is suitable for improving the machining accuracy and stability of the ball screw feed system.

The excellent performance of carbon nanotubes (CNTs) allows them to be widely employed in various micro- and nano-electromechanical devices. However, different imperfections such as Stone–Wales (S-W) defects often arise in these structures during the preparation process. In this paper, special attention is paid to the effects of the number and location of defects as well as the diameter and chiral angle of CNTs on the static and dynamic buckling of CNTs with S-W defects. First, LAMMPS software is used to simulate the molecular dynamics (MDs) of CNTs with S-W defects, and their static buckling performances are discussed. Then based on the static buckling data, the dynamic buckling vibration performance of CNTs with S-W defects is analyzed in the context of the nonlocal elastic theory. Finally, the effective range of nonlocal parameters is established via the MD modeling. The results show that the existence of S-W defects will reduce the buckling performance and vibration characteristics of CNTs, and an increase in the number of defects will aggravate the influence of diameter and chiral angle on the buckling performance as well as the natural frequency and amplitude of the nanotube’s axial vibration.