A New Model for Studying Nonlinear Vibration Behaviors of Gear-Bearing System

A new model for nonlinear vibration behaviors of gear-bearing system is proposed in this work. For presenting the nonlinear excitation from bearing compliance, the enhanced bearing force excitation model containing two kinds of bearing stiffnesses, which are mean stiffness for the load transfer capacity and alternating stiffness for the disturbance resisting ability, is developed. Considering other dynamic excitations including mesh stiffness, contact pressure angle, center distance, unbalance force caused by static and dynamic eccentricity, an advanced iterative numerical method is introduced, which can timely and accurately update the excitations caused by load-dependent and time-varying nonlinearities inside of the system. The constant bearing stiffness and time-varying bearing alternating stiffness models are introduced and compared with the enhanced bearing excitation force model. The parametric resonant regions and system nonlinear periodic motion states are studied and compared for different bearing supporting models. The effects from internal and external excitations on the system nonlinear vibration behaviors are investigated.

Optimum dog-leg angle for mass and bearing force optimization of multistage gear reduction

This paper describes a method to minimize bearing forces as well as bearing and housing mass for a multistage gear reduction. This is done by finding the optimum dog-leg angles for the stages while leaving other aspects of the design unaltered. The optimization is demonstrated first for spur gears, and then for helical gears typically used in electric vehicles. A numerical example shows how bearing forces and mass of bearings and housing are reduced considerably by choosing the optimum dog-leg angle.

Experimental Study on the Influence of Water and Cavitation on Propeller Load during Ice-Propeller Milling

When the ice-class propeller sails in an icy sea, it is affected by external factors such as water, ice, and cavitation, and the process of mutual interference is extremely complicated. In order to study the influence of water and cavitation on propeller load during the ice-propeller milling process, a test platform for ice–water propeller milling action was constructed. The load and cavitation of the propeller and single blade were measured during ice-propeller milling in air and water (atmospheric pressure and decompression conditions). Simultaneously, the changes in the load and bearing force of the propeller and blade were studied at different working conditions. The results show that, in the process of ice–water propeller milling, the direction of the propeller thrust generated by the water is opposite to that of the axial force generated by ice; the combined action of the two causes propeller thrust loss, whereas the combined action of water and ice increases propeller torque. The presence of water increases the thrust, torque, and bearing force of the fluctuating amplitude of the blade. The occurrence of cavitation reduces the thrust and torque of the propeller and blade and increases thrust fluctuating amplitudes while decreasing the tangential force fluctuating amplitude of the blade.

Research on Formation Mechanism and Suppression Method of Surface Force Caused by Pump Jet Propeller

Propeller exciting force is divided into bearing force and surface force according to the transfer path, and they are essential for radiated noise of the underwater vehicle. Surface force is an increasingly important issue in radiated noise because of the appearance of guide vanes and ducts. But the related questions about surface force are not thoroughly considered. Here we show spectral characteristics of surface force and its formation mechanism. Computational Fluid Dynamics is used in this paper. One of the important results is that there is a significant blade passing frequency (BPF) line spectrum in the radial component of surface force which does not appear in the axial direction; Another one is that the frequency amplitude at BPF of the duct is ten times that of the stator blades, which shows that the duct mainly contributes to the surface force. We also found that the amplitude of the duct surface force is equivalent to the rotor bearing force, which illustrates the importance of surface force research. It is demonstrated that the tip leakage vortex is the reason for the duct surface force by the analysis of the flow field. By adjusting the size of the tip clearance to control the tip leakage vortex, we found that the uniformity of the flow field has a significant effect on the surface force of the duct. The result obtained by this study can be used to reduce the radiated noise of underwater vehicles.

Stability and Unbalance Analysis of Rigid Rotors Supported by Spiral Groove Bearings: Comparison of Different Approaches

The dynamic behavior of spiral-grooved gas bearing supported 4DoF rotors is investigated by means of linearized bearing force coefficients and full time-integrated transient analysis. The two methods are compared for a variation of test rotors and bearing geometries in a given compressibility number interval of Lambda = [0,40]. The limitations and weaknesses of the linearized model are presented. It is shown that shafts with two symmetric herringbone-groove journal bearings have their maximum stability and load capacity if the center of gravity lays in the middle of the two bearings. For symmetric rotors (la/lb = 1) the two rigid modes, cylindrical and conical, are present and are influenced by the mass and transverse moment of inertia independently. For asymmetric rotors (la/lb < 1) the stability region decreases and the modes have a mixed shape. It is no longer possible to clearly distinguish between pure cylindrical and pure conical mode shapes. The two methods predict the critical mass and critical transverse moment of inertias within a difference of < 7%. A quasi-linear unbalance module for rigid gas bearing supported rotors is presented, which considers eccentricity dependent bearing force coefficients, allowing to speed up the unbalance response analysis by four orders of magnitude. The unbalance module is compared with the full transient orbital analysis, suggesting that the quasi-linear module predicts the non-linear unbalance response with <6% deviation for amplitudes up to e < 0.5 within the complete compressibility number range.

Vibration Response Analysis of a Gear-rotor-bearing System Considering Steady-state Temperature

As an important factor leading to the failure of gear system, the study of thermal effect is insufficiently deep. Based on the finite element nodal method, a more comprehensive dynamic model of gear-rotor-bearing system is established, which considers the thermal related material properties, time-varying meshing stiffness (TVMS), backlash and friction, gyroscopic effect. The constitutive relation of beam element considering steady-state temperature is reconstructed, and thermal node load is formulated. Considering the influence of temperature on the material properties of flexible shaft and gear, the thermal related TVMS and thermal backlash are obtained. The dynamic response of the system under different steady-state temperature fields is compared, and the influence of hot backlash is studied, then the thermal related vibration characteristics are obtained. Besides, the influence of bearing type on bearing force and axial trajectory is studied. The results show that the system motion changes from period to chaos with the temperature increase in part of the speed range. The appropriate backlash is helpful to restrain the chaotic motion caused by temperature rise. Moreover, the temperature can significantly increase the axial bearing force, and the appropriate bearing can reduce the axial displacement.

Cavitation and Induced Excitation Force of Ice-Class Propeller Blocked by Ice

The presence of broken ice in the flow field around a propeller causes severe blade erosion, shafting, and hull vibration. This study investigates the performance of the propeller of a ship sailing in the polar regions under the propeller–ice non-contact condition. To this end, we construct a test platform for the propeller-induced excitation force due to ice blockage in a large circulating water channel. The hydrodynamic load of the propeller, and the cavitation and propeller-induced fluctuating pressure, were measured and observed by varying the cavitation number and ice–propeller axial distance under atmospheric pressure and decompression conditions. The results show that the fluctuation range of the blade load increases with a decrease in cavitation number and ice–propeller axial distance. The decrease in the cavitation number leads to broadband characteristics in the frequency-domain curves of the propeller thrust coefficient and blade-bearing force. Under the combined effects of ice blockage and proximity, propeller suction, the circumfluence zone around the ice, and the Pirouette effect, propeller–hull vortex cavitation is generated between the ice and propeller. The decrease in cavitation number leads to a sharp increase in the amplitude of the high-order frequency of the propeller-induced fluctuating pressure.

Stability and Unbalance Analysis of Rigid Rotors Supported by Spiral Groove Bearings: Comparison of Different Approaches

The dynamic behavior of spiral-grooved gas bearing supported 4DoF rotors is investigated by means of linearized bearing force coefficients and full time-integrated transient analysis. The transient method consists of a state-space representation, which couples the equations of motion with the compressible thin film fluid equation. The linearized method is based on the perturbation analysis around a given eccentric shaft position ε, allowing to compute the static and linear dynamic bearing force coefficients at different excitation frequencies. The two methods are compared for a variation of test rotors and bearing geometries in a given compressibility number interval of Λ = [0,40]. The limitations and weaknesses of the linearized model are presented. It is shown that shafts with two symmetric herringbone-groove journal bearings have their maximum stability and load capacity if the center of gravity lays in the middle of the two bearings. For symmetric rotors (la/lb = 1) the two rigid modes, cylindrical and conical, are present and are influenced by the mass and transverse moment of inertia independently. For asymmetric rotors (la/lb < 1) the stability region decreases and the modes have a mixed shape. It is no longer possible to clearly distinguish between pure cylindrical and pure conical mode shapes. The two methods predict the critical mass and critical transverse moment of inertias within a difference of < 7%. A quasi-linear unbalance module for rigid gas bearing supported rotors is presented, which considers eccentricity dependent bearing force coefficients, allowing to speed up the unbalance response analysis by four orders of magnitude. The unbalance module is compared with the full transient orbital analysis, suggesting that the quasi-linear module predicts the non-linear unbalance response with < 6 % deviation for amplitudes up to ε < 0.5 within the complete compressibility number range.