Oil Film Damping Research Articles

Oil Film Damping Analysis in Non-Newtonian Transient Thermal Elastohydrodynamic Lubrication for Gear Transmission

The models of normal and tangential oil film damping are established by modeling the viscous-elastic fluid as massless damping elements. The central pressure and film thickness distributions, friction coefficient, and maximum temperature rise with or without considering thermal effect indicate the proposed damping models and the solutions to the damping are valid. Thereafter, the thermal effect on oil film damping is discussed and the effects of contact force, rotation speed, and tooth number of spur gears in line contact non-Newtonian transient thermal elastohydrodynamic lubrication (EHL) on the oil film damping are investigated. The results imply that the larger damping in the normal direction is beneficial to meshing impact resistance and vibration reduction, whereas the smaller damping in the tangential direction is very helpful for fluidity enhancement and friction heat inhibition.

Dynamic Analysis of a Rotor System Supported on Squeeze Film Damper with Air Entrainment

Squeeze film dampers (SFDs) are widely used in compressors and turbines to suppress the vibration while traversing critical speeds. In practical applications, air ingestion from the outside environment and cavitation may lead to a foamy lubricant that weakens oil film damping and dynamic performance of rotor system. In this paper, a rigid rotor model is established considering both lateral and pitching vibration under different imbalance excitations to evaluate the effect of air entrainment on rotor system. Tests with three different imbalances are carried out on a rotor-SFD apparatus. Volume controlled air in mixture ranging from pure oil to all air are supplied to the SFD. The transient response of rotor is measured in the experiments. The results show that two-phase flow produces significant influence on the system stability and dynamical response. The damping properties are weakened by entrained air, such as the damping on high frequency components of rolling ball bearing. Super-harmonic resonance and bifurcation are observed, as well as the low frequency components due to air entrainment.

The Thermohydrodynamic Analysis of Sliding Bearing High-Speed Motorized Spindle by Rotor Dynamic

This is paper presents thermohydrodynamic characteristics of high speed motorized spindle sliding bearing rotor system. The dynamic characteristic of the oil film bearing is affected by temperature increment, thereby affecting the high-speed spindle rotor system dynamics. This study applied the hydrodynamic lubrication theory, the influence of temperature on the viscosity of lubricating oil, associated with the bearing stiffness, oil film damping and other performance parameters, is considered in generalized Reynolds equation of oil film bearing. The theoretical model of the sliding bearing rotor system is established by using the transfer matrix method to analyze the dynamic characteristic and verified by experiments. The results show the high temperature environment in the motorized spindle and the friction of the bearing lead to oil temperature rise and viscosity reduction, which influences the bearing capacity, stiffness and damping, hence impact on the critical speeds and modal shapes of the sliding bearing rotor system.

Oil film stiffness and damping in an elastohydrodynamic lubrication line contact-vibration

An elastohydrodynamic lubrication line contact-vibration model is proposed to study the stiffness and damping of the oil film existed in the EHL contact region. An initial mutual approach between interacting surfaces, which deviates from the steady-state balanced position, is assumed under the free contact-vibration to predict the response of the mutual approach. An inertia term, which represents the acceleration of the gap motion, is added to the classical force balance equation to form the equation of motion of the mutual approach. Response of the mutual approach is solved based upon the solving of the contact-dynamic model. The oil stiffness is calculated according to the natural frequency of the response under damped and non-damped conditions, the latter of which represents dry contact conditions. The oil film damping is calculated in terms of the principle of the energy conservation which utilizes the whole history of response compared with the log decrement method. Effect of the normal load, the rolling speed and the amplitude of the regular sinusoidal surface waviness on the oil film stiffness, the contact stiffness and the oil film damping are studied. The study provides an insight on the oil film dynamic characteristics of lubricated contact-vibration problems which appear in gears, bearings, etc. The results show that the oil film damping factor decreases with the increasing normal load as well as the increasing rolling speed. The oil film stiffness increases with the normal load and decreases with the rolling speed. Also, compared to the contact stiffness, the oil film stiffness makes less contribution to the total stiffness. The surface waviness amplitude has little effect on the oil film stiffness and the oil film damping.

Theoretical and experimental studies on dynamics of double-helical gear system supported by journal bearings

The dynamic behaviour of a double-helical gear system supported by journal bearings is theoretically and experimentally investigated in this study. A bending–torsional–axial coupling model for dynamic analysis of double-helical gear system is developed. Influence of the time-varying mesh stiffness and damping is considered. Oil film stiffness and damping of the supporting journal bearing are supposed to be time-varying, and the time-varying oil film stiffness and damping are predicted by a back propagation neural network, which is optimized by genetic algorithm. A double-helical gear–rotor–journal bearing system test rig is also established to carry out the experimental investigations, such as the dynamic transmission errors of gear pairs. The comparisons between theoretical and experimental results show that the time-varying oil film dynamic coefficients of journal bearings are an important internal excitation. The theoretical model with time-varying oil film stiffness and damping can predict the gear dynamics more accurate than the model with time-invariant oil film stiffness and damping, and the neural network optimized by genetic algorithm can obtain the time-varying oil film stiffness and damping efficiently and accurately for the dynamic analysis of double-helical gear system.

Elastic ring deformation and pedestal contact status analysis of elastic ring squeeze film damper

This paper investigates the dynamic parametric characteristic of the elastic ring squeeze film damper (ERSFD). Firstly, the coupled oil film Reynolds equations and dynamic equations of an ERSFD supported rotor system are established. The finite differential method and numerical simulation are used to analyze the oil film pressure distribution, bearing capacity of ERSFD, oil film stiffness and damping characteristics during a vibration period. Then, based on the oil film pressure results, the deformation of elastic ring is revealed by the finite element method. Finally, pedestal contact status is analyzed according to the change of oil film thickness during a vibration period. The results reveal that the oil film pressure is sectionally continuous, the deformation of elastic ring is complex under the compression of inner and outer oil film, and different pedestal contacts occur in a vibration period. The level of nonlinearity of the bearing capacity, oil film stiffness and damping can be effectively lightened by application of the elastic ring.

Propeller Excitation of Longitudinal Vibration Characteristics of Marine Propulsion Shafting System

The submarine experiences longitudinal vibration in the propulsion shafting system throughout most of run. A transfer matrix model of the propulsion shafting system, in which the dynamic characteristics of oil film within thrust bearing are considered, is established to describe the dynamic behavior. Using hydrodynamic lubrication theory and small perturbation method, the axial stiffness and damping of oil film are deduced in great detail, followed by numerical estimation of the foundation stiffness with finite element method. Based upon these values of dynamic parameters, the Campbell diagram describing natural frequencies in terms of shafting rotating speeds is available, and the effect on the 1st natural frequency of considerable variations in thrust bearing stiffness is next investigated. The results indicate that the amplitude of variation of the 1st natural frequency in range of low rotating speeds is great. To reduce off-resonance response without drastic changes in propulsion shafting system architecture, the measure of moving thrust bearing backward is examined. The longitudinal vibration transmission through propulsion shafting system results in subsequent axial excitation of hull; the thrust load acting on hull is particularly concerned. It is observed that the measures of structural modification are of little benefit to minimize thrust load transmitted to hull.

Squeeze Oil-Film Fluid-Structure Interaction Analysis by the Finite Element Method

The squeeze oil-film dampers have been applied to damp out vibration in linear guideway systems of CNC machine tools. An accurate estimate of squeeze oil-film damping effects is significant to predict the dynamic performance of rolling guidance systems. This paper presents a finite element method to solve the fluid-structure interaction problem of squeeze oil-film dampers. Three-node Mindlin plate element is used in the structure domain model. The oil-film behavior is provided by the Reynolds equation of lubrication theory. Both the structural domain and fluid domains are discretized by finite element method. The frequency response functions of coupled systems are derived by considering the oil-film pressures and the structure displacements on the boundary as the coupling conditions. The validity of the frequency response functions is verified by a simple example. It shows that the oil-film thickness has significant influence on the frequency response.

Rotordynamic model for electromagnetic excitation caused by an eccentric and angular rotor core in an induction motor

The paper shows a rotordynamic model for electromagnetic excitation caused by an eccentric and angular rotor core in an induction motor. It is shown that an eccentric rotor core leads to an electromagnetic force and an angular rotor core to an electromagnetic moment, which both force the rotor to vibrate. For these two kinds of magnetic unbalance, a rotordynamic model was developed considering the influence of the oil film stiffness and damping of the sleeve bearings, the stiffness of the end-shields and bearing housings, the stiffness of the rotor, the electromagnetic stiffness—radial and angular electromagnetic stiffness—the mass moment of inertia and the gyroscopic effect of the rotor. With this model, the absolute orbits of the shaft centre, the shaft journals and the bearing housings can be calculated, as well as the relative orbits between the shaft journals and the bearing housings. Additionally, the bearing housing velocities can also be computed. In addition to the mathematical derivation of the model, also a numerical example is shown for clarification. The aim of the paper is, on the one hand, to show the mathematical coherences—based on an analytical model—between rotordynamics and the electromagnetics for an induction motor with an eccentric and angular rotor core and, on the other hand, to derive a calculation method for evaluating the vibration sensitivity regarding these two different kinds of magnetic unbalance.

Vibrations caused by noncircular shaft journals — a mathematical model for rotordynamic analysis of electrical motors with sleeve bearings

The paper presents a mathematical model for theoretical rotordynamic analysis of electrical motors with sleeve bearings, regarding excitation due to noncircular shaft journals. It is shown, that noncircular shaft journals lead to kinematic constraints regarding the movement of the shaft journals on the oil film of the sleeve bearings and therefore excite the rotordynamic system to vibrate. The rotordynamic system is mathematically described by a system of linear differential equations, considering the rotor mass, the rotor structural stiffness, the oil film stiffness and damping of the sleeve bearings, the structural stiffness of the sleeve bearing housings with the end shields, the electromagnetic coupling between rotor and stator in the air gap and the excitation due to noncircular shaft journals. The solution of this differential equation system leads to the mathematical description of the movement of the rotor centre, the shaft journals and the sleeve bearing housings. Additionally, the relative movements between the shaft journals and the bearing housings can be calculated, as well as the bearing housing vibration velocities. A four-pole induction motor is analyzed, to also show numerical results.

Mathematical Rotordynamic Model Regarding Excitation Due to Elliptical Shaft Journals in Electrical Motors Considering the Gyroscopic Effect

The paper presents a mathematical rotordynamic model regarding excitation due to elliptical shaft journals in sleeve bearings of electrical motors also considering the gyroscopic effect. For this kind of excitation, a mathematical rotordynamic model was developed considering the influence of the oil film stiffness and damping of the sleeve bearings, the stiffness of the end-shields and bearing housings, the stiffness of the rotor, the electromagnetic stiffness in the air gap of the electrical motor and the mass moment of inertia of the rotor and therefore also considering the gyroscopic effect. The solution of the linear differential equation system leads to the mathematical description of the absolute orbits of the shaft centre, the shaft journals and the bearing housings and to the relative orbits between the shaft journals and the bearing housings. Additionally, the bearing housing velocities can also be derived with this mathematical rotordynamic model.

Design and Performance Assessment of a 5-Axis Ultra-Precision Micro-Milling Machine

This paper presents the development and performance assessment of a novel 5-axis ultra-precision micro-milling machine (UltraMill) which enables ultra-precision micromachining of high precision 3D miniature components and micro features. An integrated design approach with motion accuracy, dynamic stiffness and thermal stability prioritized has been proposed and applied to analyze and optimize key machine components and their integration. Direct drives and aerostatic bearings with the squeeze oil-film damper are employed in the micro-milling machine throughout, which offers higher motion accuracy, improved dynamics and loading capacity. Micro-milling trials were performed on OFHC copper using tungsten carbide, CVD diamond and single crystal diamond micro tools. Both micro featured profiles and micro machined surfaces were measured to validate the proposed machine specifications and performance.

Finite Element Analysis on Dynamic Characteristics of Hybrid Bearing Spindle System

Due to having the features of high accuracy, high stiffness, high load capacity and longer service life, the hybrid bearing spindle system is widely used in grinding. This paper presents an analysis method of hybrid bearing spindle dynamic characteristics. The method uses CFD method to solve the oil film pressure field, instead of Reynolds equation, in order to obtain the oil film stiffness and damping. With the obtained oil film stiffness and damping to build the appropriate constraints, 3D finite element model of the hybrid bearing spindle system is established, and the modal analysis of the spindle system is carried out. Compared the analysis results with the theoretical calculation results, the feasibility and correction of the method are proved.

Dynamic stability analysis of cages in high-speed oil-lubricated angular contact ball bearings

To investigate the cage stability of high-speed oil-lubricated angular contact ball bearings, a dynamic model of cages is developed on the basis of Gupta’s and Meeks’ work. The model can simulate the cage motion under oil lubrication with all six degrees of freedom. Particularly, the model introduces oil-film damping and hysteresis damping, and deals with the collision contact as imperfect elastic contact. In addition, the effects of inner ring rotational speed, the ratio of pocket clearance to guiding clearance and applied load on the cage stability are investigated by simulating the cage motion with the model. The results can provide a theoretical basis for the design of ball bearing parameters.

Effects of Angular Spring and Angular Damping of Oil Film on Stability Characteristics of Flexible Rotor Supported in Journal Bearings

This paper shows the stability characteristics of a flexible rotor supported in three types of multi-lobe bearings, i.e. 2-lobe bearings, 3-lobe bearings and 4-lobe bearings, and tilting pad journal bearings theoretically. Angular spring and angular damping coefficients of oil film of the bearings are calculated and the effects of the preload factor on the coefficients are discussed. With a Jeffcott rotor model considering the angular spring and angular damping coefficients, stability charts are made under the wide range of operating conditions, and show that 2-lobe bearings with a high preload factor cover much larger stable region in the stability charts than the other bearings, and 3-lobe bearings, 4-lobe bearings and tilting pad journal bearings with line contact pivots do not have special advantages in comparison with 2-lobe bearings. From the results, it is concluded that 2-lobe bearings with a high preload factor are most suitable for supporting the flexible rotor.

On the non-linear dynamic behavior of elastohydrodynamic lubricated point contact

The complex dynamic concepts of mechanical systems are regarded each day as new barriers to be overcome. One of the most complex systems, despite its common construction design, is the rolling element bearings. The interactive dynamic interfaces of such bearings are normally disregarded by engineering analysis on the day to day basis due to its complexities. This paper intends to propose a new approach to the characterization of the elastohydrodynamic lubricated point contacts on such components, in order to fully depict its non-linear dynamic behavior, avoiding the use of rough hypothesis on a systemic procedure. A multi-level method was used to solve the coupled lubrication–deformation problem, alongside a Newmark-ß integrator of the motion equation for the contact system. A range of dynamically similar contacts were evaluated, so as to characterize its nonlinear dynamic behavior. A least-squares method was applied to the multi-level algorithm results, fitting the displacements–force relation to a linear and also to a third order polynomial stiffness. The fitting results were compared, clearly showing the nonlinear behavior of such contacts. Also, the oil film damping was regarded as viscous, leading to good overall response. Some peculiarities of the proposed adjust method are also considered.

Finite element analysis of a soft mounted 2-pole asynchronous machine concerning vibration stability

The paper describes a finite element calculation concerning vibration stability of a 2-pole asynchronous machine with sleeve bearings and flexible shaft, mounted on soft foundation elements. The finite element model considers the rotor, stator, end shields and bearing housings, oil film stiffness and damping, the electromagnetic interaction between rotor and stator – deduced from an electromagnetic field calculation -, the gyroscopic effect of the rotor and the influence of the foundation stiffness and damping. The critical mode shapes and natural frequencies are calculated for different rotor speeds and the eigenvalues are analyzed to receive the limit of stability. Therefore the paper shows a calculation method to optimize the vibration stability by considering foundation stiffness and damping.

Study on Squeeze Oil Film Damper in Ultrahigh Speed Grinding

The operation principle of SFD and the center moving orbit of grinding wheel spindle which under the operation of SFD are studied. Based on the theoretical research, the experiment is studied and analyzed. The study results show that the application of SFD technology can effectively restrain vibration which is caused by the imbalance quality when the grinding wheel spindle turning at ultrahigh speed. And it can remarkably improve the working quality and work efficiency of ultra high-speed grinder.

Effect of Angular Spring and Angular Damping of Oil Film on the Stability Characteristics of Tilting-Pad Journal Bearings

Effect of Angular Spring and Angular Damping of Oil Film on the Stability Characteristics of Tilting-Pad Journal Bearings

A Study of Crankshaft Vibration Mechanism in Operation. Visualization of the Vibration Mechanism by means of Time History Response Analysis is Consideration of Nonlinearity of Oil film.

The vibration behavior of the crankshaft in operation is complex to simulate because there are many contributing factors, some of which are varying, oil film stiffness and damping, coupled vibration of the rotating crank train and cylinder block. This paper describes a new method of analyzing the nonlinear vibration of rotating crank train, in which calculations are made of using nonlinear equation of motion. This method uses stiffness and mass matrices of the component parts, which have been extracted from the finite element model using in-house software. The coupled vibration of the rotating crankshaft and cylinder block is calculated by means of time history response analysis, in sonsideration of the non-linearity of the oil film stiffness, damping and friction. The accuracy of this calculation technique was demonstrated by comparing the calculated results with the actual vibration measured with LASER equipment.