scholarly journals Dynamics Modeling and Experimental Investigation of Gear Mechanism with Coupled Small Clearances

Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 834
Author(s):  
Jianchao Han ◽  
Lei Liang ◽  
Huibo Zhang ◽  
Yang Zhao
Keyword(s):  
Coupled Model ◽  
Rotor System ◽  
Radial Clearance ◽  
Force Model ◽  
Dynamics Modeling ◽  
Compact Structure ◽  
Light Load ◽  
Small Clearance ◽  
Gear Mechanism ◽  
Internal Gear

Internal gear mechanism is widely used in micro-nano satellites due to its compact structure and high precision transmission. However, the vibration coupling caused by the small clearance coupling is more obvious and cannot be ignored under low speed, light load and zero gravity conditions. Based on the geometric relationship between radial clearance and backlash, a coupled model between dynamic backlash and radial clearance of internal meshing gear is established. Based on the conformal contact theory, the radial collision force model of the gear shaft and shaft sleeve considering the small clearances is established. Additionally, a multi-clearance gear rotor system test device is built to measure the vibration acceleration of the internal gear rotor system by an acceleration sensor and transmitted to the industrial computer through a signal collector for data processing. Through the comparison of simulation and experiment, the accuracy of the gear dynamics model is verified. The analysis results show that, compared with the traditional model, the calculation results of the gear mechanism model considering the small clearance coupling is closer to the experimental data.

scholarly journals Model Dimension Reduction and Nonlinear Analysis of the Sprag Clutch-flexible Rotor System Considering Local Nonlinearity

2020 ◽  
Author(s):  
Chuang Huang ◽  
Yongqiang Zhao ◽  
Guanghu Jin
Keyword(s):  
Dimension Reduction ◽  
Synthesis Method ◽  
Rotor System ◽  
Hertzian Contact ◽  
Radial Clearance ◽  
System Response ◽  
Force Model ◽  
Flexible Rotor ◽  
Interface Synthesis ◽  
Fixed Interface

Abstract In order to study the influence of local nonlinear factors such as bearing clearance and Hertzian contact on the nonlinear behavior of the sprag clutch-rotor system during high-speed steady-state engaging, a nonlinear force model of rolling bearing considering radial clearance and Hertzian contact is established. Regarding the inner and outer rotors as substructures, the fixed interface modal synthesis method is used to reduce the dimension of the substructure model, and the nonlinear dimension reduction model of the sprag clutch-flexible rotor system (SC-FRS) is obtained. To improve computational efficiency, the Newmark method combined with the fixed interface synthesis method is presented to calculate the system response. The response results of the reduced model with a different number of dominant modes and the unreduced model are compared, and the number of reserved dominant modes of the inner and outer rotors is selected based on the calculation efficiency and accuracy. The effect of the radial clearance of different bearings on the nonlinear vibration response and the dynamic load of the inter-shaft bearing is discussed. It is found that the sensitivity of different radial clearances to the system's amplitude-frequency response is different, and the amplitude jump and the frequency hysteresis appear at the resonance peak.

scholarly journals Experimental and Numerical Investigation about Small Clearance Journal Bearings under Static Load Conditions

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Carlo Alberto Niccolini Marmont Du Haut Champ ◽  
Fabrizio Stefani ◽  
Paolo Silvestri
Keyword(s):  
Three Dimensional ◽  
Journal Bearings ◽  
Radial Clearance ◽  
Small Scale ◽  
Test Rig ◽  
Small Clearance ◽  
Dimensional Simulation ◽  
Dynamic Loading Conditions ◽  
Static And Dynamic Loading ◽  
Good Agreement

The aim of the present research is to characterize both experimentally and numerically journal bearings with low radial clearances for rotors in small-scale applications (e.g., microgas turbines); their diameter is in the order of ten millimetres, leading to very small dimensional clearances when the typical relative ones (order of 1/1000) are employed; investigating this particular class of journal bearings under static and dynamic loading conditions represents something unexplored. To this goal, a suitable test rig was designed and the performance of its bearings was investigated under steady load. For the sake of comparison, numerical simulations of the lubrication were also performed by means of a simplified model. The original test rig adopted is a commercial rotor kit (RK), but substantial modifications were carried out in order to allow significant measurements. Indeed, the relative radial clearance of RK4 RK bearings is about 2/100, while it is around 1/1000 in industrial bearings. Therefore, the same original RK bearings are employed in this new test rig, but a new shaft was designed to reduce their original clearance. The new custom shaft allows to study bearing behaviour for different clearances, since it is equipped with interchangeable journals. Experimental data obtained by this test rig are then compared with further results of more sophisticated simulations. They were carried out by means of an in-house developed finite element (FEM) code, suitable for thermoelasto-hydrodynamic (TEHD) analysis of journal bearings both in static and dynamic conditions. In this paper, bearing static performances are studied to assess the reliability of the experimental journal location predictions by comparing them with the ones coming from already validated numerical codes. Such comparisons are presented both for large and small clearance bearings of original and modified RKs, respectively. Good agreement is found only for the modified RK equipped with small clearance bearings (relative radial clearance 8/1000), as expected. In comparison with two-dimensional lubrication analysis, three-dimensional simulation improves prediction of journal location and correlation with experimental results.

scholarly journals Influence of radial clearance on nonlinear dynamics of a two-span three-support rotor system

2021 ◽  
Vol 233 ◽  
pp. 04012
Author(s):  
HE Xing ◽  
WU Yi-ming ◽  
LI Mo ◽  
ZENG Fan
Keyword(s):  
Periodic Motion ◽  
Rotor System ◽  
System Model ◽  
Radial Clearance ◽  
Structural Form ◽  
Single Cycle ◽  
Rolling Bearings ◽  
System A ◽  
Runge Kutta Method ◽  
Nonlinear Dynamic Characteristics

Aiming at the structural form of a certain rotor system, a double-span three-support rotor system model is established. It is supported by three rolling bearings and has a typical nonlinear characteristic. The fourth-order Runge-Kutta method is used to solve the differential equations and analyze the nonlinear dynamic characteristics of the rotor system when the radial clearance of the bearing changed. The research results: with the increase of the rear bearing radial clearance, the rotor system performs single cycle, periodic two and pseudo-periodic motion. With the three location bearing radial clearance increases, the rotor system performs single cycle, periodic two and periodic four motion. When the radial clearance is bigger, the rotor system performs two periodic motion. The influence law of radial clearance on double span three - braced rotor system is shown.

Dynamic Analysis of a Coupled Dual-Rotor With Squeeze Film Damper Considering Sudden Unbalance

2021 ◽  
Author(s):  
Ying Cui ◽  
Yuxi Huang ◽  
Guogang Yang ◽  
Yongliang Wang ◽  
Han Zhang
Keyword(s):  
Steady State ◽  
Transient Response ◽  
Rotor System ◽  
Lubricating Oil ◽  
Squeeze Film ◽  
Radial Clearance ◽  
Oil Viscosity ◽  
Squeeze Film Damper ◽  
Damping Effect ◽  
Bistable State

Abstract A nonlinear multi-degree-of-freedom dynamic model of a coupled dual-rotor system with an intershaft bearing and uncentralized squeeze film damper is established by using finite element method. Based on the model, the critical speed characteristic diagram and vibration modes of the system were calculated. The steady-state unbalance response is obtained by using Newmark-β algorithm. The numerical results show the effect of SFD position in the dual-rotor system on response amplitude. It is found that with the decrease of radial clearance and the increase of length-diameter ratio and lubricating oil viscosity, the damping effect of SFD is enhanced and the bistable state phenomenon can be suppressed. The transient response of the system in case of sudden unbalance occurring at the fan was simulated by applying a step function. It is demonstrated that the SFD can effectively reduce the duration and maximum amplitude of the transient process, but at certain speeds, the SFD will increase the amplitude after the system returns to steady state, the damping effect on the transient response is also enhanced with the increase of length-diameter and the decrease of radial clearance, and with the increase of the sudden unbalance value, the response is more likely to stabilized at the high amplitude state of the bistable state.

A Coupled Thermomechanical Modeling Method for Predicting Grinding Residual Stress Based on Randomly Distributed Abrasive Grains

2019 ◽  
Vol 141 (8) ◽  
Author(s):  
Zhenguo Nie ◽  
Gang Wang ◽  
Liping Wang ◽  
Yiming (Kevin) Rong
Keyword(s):  
Residual Stress ◽  
Coupled Model ◽  
Grinding Force ◽  
Modeling Method ◽  
Temperature Fields ◽  
Force Model ◽  
Thermomechanical Model ◽  
Abrasive Wheel ◽  
Abrasive Grains ◽  
Thermomechanical Modeling

Abstract In this research, we propose a coupled thermomechanical modeling method for predicting grinding residual stress based on randomly distributed grains. In order to deal with the problem that the nominal grinding force is too small to generate the plastic deformation, we hold the opinion that grinding residual stress is totally derived from three factors: thermal stress, the nominal grinding force (pressure) over the entire grinding zone, and the equivalent plowing force just under the bottom of the abrasive wheel. Finite element model (FEM) simulation of the single-grain grinding (SGG) is conducted to obtain the critical plowing depth and the SGG force at an arbitrary cutting depth. Based on the randomly distributed abrasive grains, the equivalent grinding heat source model, the equivalent SGG plowing force model, and the equivalent nominal pressure model are all established. A 2D coupled thermomechanical model is established to simulate the grinding process for temperature fields and grinding residual stress fields. In addition, verification tests are conducted to validate the model. It turns out that the coupled model can accurately predict the multiphysical fields on both temperature and residual stress. Based on the simulation results of the model, the generation mechanism of grinding residual stress is quantitatively studied. This research provides a promising pathway to residual stress control of grinding.

scholarly journals Development of a new test rig for the analysis of hydrodynamic bearings for rotors of microGT

2019 ◽  
Vol 113 ◽  
pp. 03002
Author(s):  
Carlo Alberto Niccolini Marmont Du Haut Champ ◽  
Fabrizio Stefani ◽  
Paolo Silvestri
Keyword(s):  
Experimental Data ◽  
Finite Element ◽  
Gas Turbines ◽  
Dynamic Interaction ◽  
Journal Bearings ◽  
Radial Clearance ◽  
Test Rig ◽  
Small Clearance ◽  
Stiffness And Damping ◽  
Good Agreement

The aim of the present work is to design a test rig suited to investigate the dynamic interaction between rotor and hydrodynamic journal bearings in micro gas turbines (microGT), i.e. with reference to small bearings (diameter in the order of ten millimeters). Particularly, the device is capable of measuring the journal location. Therefore, the journal motion due to rotor vibrations can be displayed, in order to assess performance as well as stiffness and damping of the bearings. The new test rig is based on Bently Nevada Rotor Kit (RK), but substantial modifications are carried out. Indeed, the relative radial clearance of the original RK bearings is about 2/100, while it is in the order of 1/1000 in industrial bearings. Therefore, the same RK bearings are employed in the new test rig, but a new shaft has been designed in order to reduce the original clearance. The new shaft enables us to study the bearing behaviour for different clearances, as it is equipped with interchangeable journals. The experimental data yielded by the new test rig are compared with numerical results. These are obtained by means of a suitable finite element (FEM) code developed by our research group. It allows the Thermo Elasto-HydroDynamic (TEHD) analysis of the bearing in static and dynamic conditions. In the present paper, bearing static performances are analysed in order to assess the reliability of the journal location predictions by comparing numerical and experimental results. Such comparisons are presented for both large and small clearance bearings of original and modified RK, respectively. Good agreement is found only for the modified RK equipped with small clearance bearings (relative radial clearance equal to 8/1000). Nevertheless, rotor alignment is quite difficult with small clearance bearings and a completely new test rig is designed for future experiments.

scholarly journals Quasi-Static Characteristics and Vibration Responses Analysis of Helical Geared Rotor System with Random Cumulative Pitch Deviations

2020 ◽  
Vol 10 (12) ◽  
pp. 4403
Author(s):  
Bing Yuan ◽  
Geng Liu ◽  
Lan Liu
Keyword(s):  
Degrees Of Freedom ◽  
Transmission Error ◽  
Rotor System ◽  
Dynamic Responses ◽  
Contact Ratio ◽  
Tooth Contact Analysis ◽  
Long Period ◽  
Light Load ◽  
Vibration Responses ◽  
Loaded Tooth Contact Analysis

As one of the long period gear errors, the effects of random cumulative pitch deviations on mesh excitations and vibration responses of a helical geared rotor system (HGRS) are investigated. The long-period mesh stiffness (LPMS), static transmission error (STE), as well as composite mesh error (CMS), and load distributions of helical gears are calculated using an enhanced loaded tooth contact analysis (LTCA) model. A dynamic model with multi degrees of freedom (DOF) is employed to predict the vibration responses of HGRS. Mesh excitations and vibration responses analysis of unmodified HGRS are conducted in consideration of random cumulative pitch deviations. The results indicate that random cumulative pitch deviations have significant effects on mesh excitations and vibration responses of HGRS. The curve shapes of STE and CMS become irregular when the random characteristic of cumulative pitch deviations is considered, and the appearance of partial contact loss in some mesh cycles leads to decreased LPMS when load torque is relatively low. Vibration modulation phenomenon can be observed in dynamic responses of HGRS. In relatively light load conditions, the amplitudes of sideband frequencies become larger than that of mesh frequency and its harmonics (MFIHs) because of relatively high contact ratio. The influences of random cumulative pitch deviations on the vibration responses of modified HGRS are also discussed.

Coupled Bending-Torsional Vibration Analysis of Rotor System with Two Asymmetric Disks

2011 ◽  
Vol 130-134 ◽  
pp. 2335-2339
Author(s):  
Jun Hong Zhang ◽  
Zhen Peng He ◽  
Wen Peng Ma ◽  
Liang Ma ◽  
Gui Chang Zhang
Keyword(s):  
Phase Difference ◽  
Vibration Analysis ◽  
Initial Phase ◽  
Rotor System ◽  
Dynamic Equations ◽  
Force Model ◽  
Torsional Angle ◽  
Kutta Method ◽  
Internal Damping ◽  
Initial Phase Difference

The dynamic equations derived based on the actual rotor system with two asymmetric disks. In the analysis, the eccentric, rubbing fault characteristics and internal damping effects is considered, and all the analysis is established based on nonlinear oil film force model and coupled bending-torsional differential equations. The Rugge-Kutta method is used to solve numerical model, the torsional displacement response, torsion angle and Poincare map are obtained. The results show torsion amplitudes with initial phase difference π / 2 is larger than initial phase difference of π and 0. In order to eliminate the rigid rolling component the relative torsional angle must be considered.

Effect of Rim Thickness on Tooth Root Stress and Mesh Stiffness of Internal Gears

2014 ◽  
Author(s):  
F. Karpat ◽  
B. Engin ◽  
O. Dogan ◽  
C. Yuce ◽  
T. G. Yilmaz
Keyword(s):  
Weight Ratio ◽  
Planetary Gear ◽  
Mesh Stiffness ◽  
Gear Mesh ◽  
Aerospace Applications ◽  
Bending Stresses ◽  
Gear Mechanism ◽  
Internal Gear ◽  
Gear Mesh Stiffness ◽  
Root Stress

In recent years, internal gears are used commonly in a number of automotive and aerospace applications especially in planetary gear drives. Planetary gears have many advantages such as compactness, large torque-to-weight ratio, large transmission ratios, reduced noise and vibrations. Although internal gears have many advantages, there are not enough studies on it. Designing an internal gear mechanism includes two important parameters. The gear mesh stiffness which is the main excitation source of the system. In this paper, 2D gear models are developed in order to compute gear mesh stiffness for various rim thicknesses and different rim shapes of the internal gear design. Effects of root stress with varying rim thickness and some tooth parameters are investigated by using 2D gear models. The stress calculated according to ISO 6336 and the stresses calculated against FEM are compared. These results are well-matched. It is observed that when the rim thicknesses are increased, both the maximum bending stresses and gear mesh stiffness are decreased considerably.

Compliant Force Modelling for Impact Analysis

2004 ◽  
Author(s):  
Yuning Zhang ◽  
Inna Sharf
Keyword(s):  
Contact Force ◽  
Impact Analysis ◽  
Nonlinear Damping ◽  
Simple Expression ◽  
Contact Dynamics ◽  
Damping Coefficient ◽  
Force Model ◽  
Dynamics Modeling ◽  
Contact Phase ◽  
New Research

Contact dynamics modeling remains an intensive area of research with new applications emerging in robotics, biomechanics and multibody dynamics areas. Many formulations for contact dynamics problem have been proposed. The two most prominent categories include the discrete approach, which employs the impulse-momentum relations, and the continuous approach, which requires integration of dynamics equations through the contact phase. A number of methods in the latter category are based on an explicit compliant model for the contact force. One such model was developed by Hunt and Crossley three decades ago who introduced a nonlinear damping term of the form λxnx˙ into the contact force model. In addition to proposing the general form of this damping component of the contact force, Hunt and Crossley derived a simple expression for relating the damping coefficient λ to the coefficient of restitution e. This model gained considerable popularity due to its simplicity and realistic physics. It also spurred new research in the area, specifically on how to evaluate the damping coefficient λ. Subsequently, several authors put forward different approximations for λ, however, without clearly revealing the range of validity of their simplifying assumptions or the accuracy limitations of the resulting contact force models. The authors of this paper analyze the various approaches employed to derive the damping coefficient. We also evaluate and compare performance of the corresponding models by using a meaningful measure for their accuracy. A new derivation is proposed to calculate more precisely the damping coefficient for the nonlinear complaint contact model. Numerical results comparing all models are presented for a sphere dropping on a stationary surface.

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