A Dynamic Absorber for Gear Systems Operating in Resonance and Instability Regions

1981 ◽  
Vol 103 (2) ◽  
pp. 364-371
Author(s):  
M. Benton ◽  
A. Seireg
Keyword(s):  
Design Stage ◽  
Optimal Parameters ◽  
Mesh Stiffness ◽  
Pinion Gear ◽  
Optimal Dynamic ◽  
Instability Regions ◽  
Dynamic Absorber ◽  
High Dynamic ◽  
Gear Systems ◽  
Stiffness And Damping

There are many practical situations where resonances and instabilities in pinion-gear systems are difficult to predict in the design stage due to the unreliability of estimating the mesh stiffness and damping parameters. This paper presents a procedure for the design of an optimal dynamic absorber system which can be used in conditions where preliminary analysis shows that high dynamic tooth loads are likely to occur. The optimal parameters for the absorber are given in a generalized form in order to simplify its design for a particular gear system.

Mesh Stiffness Variation Instabilities in Two-Stage Gear Systems

2001 ◽  
Author(s):  
Jian Lin ◽  
Robert G. Parker
Keyword(s):  
Numerical Solutions ◽  
Parametric Instability ◽  
Operating Conditions ◽  
Mesh Stiffness ◽  
Two Stage ◽  
Instability Regions ◽  
Stiffness Variation ◽  
Parametric Instabilities ◽  
Gear Systems ◽  
Mesh Phasing

Abstract Mesh stiffness variation, the change in stiffness of meshing teeth as the number of teeth in contact changes, causes parametric instabilities and severe vibration in gear systems. The operating conditions leading to parametric instability are investigated for two-stage gear chains, including idler gear and countershaft configurations. Interactions between the stiffness variations at the two meshes are examined. Primary, secondary, and combination instabilities are studied. The effects of mesh stiffness parameters, including stiffness variation amplitudes, mesh frequencies, contact ratios, and mesh phasing, on these instabilities are analytically identified. For mesh stiffness variation with rectangular waveforms, simple design formulae are derived to control the instability regions by adjusting the contact ratios and mesh phasing. The analytical results are compared to numerical solutions.

Mesh Stiffness Variation Instabilities in Two-Stage Gear Systems

2001 ◽  
Vol 124 (1) ◽  
pp. 68-76 ◽  
Author(s):  
Jian Lin ◽  
Robert G. Parker
Keyword(s):  
Numerical Solutions ◽  
Parametric Instability ◽  
Operating Conditions ◽  
Mesh Stiffness ◽  
Two Stage ◽  
Instability Regions ◽  
Stiffness Variation ◽  
Parametric Instabilities ◽  
Gear Systems ◽  
Mesh Phasing

Mesh stiffness variation, the change in stiffness of meshing teeth as the number of teeth in contact changes, causes parametric instabilities and severe vibration in gear systems. The operating conditions leading to parametric instability are investigated for two-stage gear chains, including idler gear and countershaft configurations. Interactions between the stiffness variations at the two meshes are examined. Primary, secondary, and combination instabilities are studied. The effects of mesh stiffness parameters, including stiffness variation amplitudes, mesh frequencies, contact ratios, and mesh phasing, on these instabilities are analytically identified. For mesh stiffness variation with rectangular waveforms, simple design formulas are derived to control the instability regions by adjusting the contact ratios and mesh phasing. The analytical results are compared to numerical solutions.

Simulation of Resonances and Instability Conditions in Pinion-Gear Systems

1978 ◽  
Vol 100 (1) ◽  
pp. 26-32 ◽  
Author(s):  
M. Benton ◽  
A. Seireg
Keyword(s):  
Phase Plane ◽  
Operating Conditions ◽  
Steady State Response ◽  
Mesh Stiffness ◽  
State Response ◽  
Convenient Means ◽  
Pinion Gear ◽  
Phase Plane Method ◽  
Gear Systems ◽  
Set Up

This paper describes a computer simulation procedure based on the phase-plane method for predicting the steady-state response, resonances and instabilities of pinion-gear systems subjected to sinusoidal excitation. An experimental technique is also presented which is capable of checking the accuracy of the simulation under different operating conditions. The experimental set-up which utilizes a shaker for producing variations of mesh stiffness without complete rotation of the gear pair provides a relatively simple and convenient means for investigating this class of problems.

scholarly journals Geometry Modification of Helical Gear for Reduction of Static Transmission Error

2018 ◽  
Vol 167 ◽  
pp. 02013
Author(s):  
Jeonghyun Park ◽  
Changjun Seo ◽  
Kwangsuck Boo ◽  
Heungseob Kim
Keyword(s):  
Transmission Error ◽  
Helical Gear ◽  
Necessary Condition ◽  
Mesh Stiffness ◽  
Profile Modification ◽  
Gear Mesh ◽  
Static Transmission Error ◽  
Excitation Mechanisms ◽  
Gear Systems ◽  
Gear Mesh Stiffness

Gear systems are extensively employed in mechanical systems since they allow the transfer of power with a variety of gear ratios. So gears cause the inherent deflections and deformations due to the high pressure which occurs between the meshing teeth when transmit power and results in the transmission error. It is usually assumed that the transmission error and variation of the gear mesh stiffness are the dominant excitation mechanisms. Predicting the static transmission error is a necessary condition to reduce noise radiated from the gear systems. This paper aims to investigate the effect of tooth profile modifications on the transmission error of helical gear. The contact stress analysis was implemented for different roll positions to find out the most critical roll angle in view point of root flank stress. The PPTE (peak-to-peak of transmission error) is estimated at the roll angles by different loading conditions with two dimensional FEM. The optimal profile modification from the root to the tip is proposed.

Effect of the bearing clearance on vibrations of a double-row planetary gear system

2019 ◽  
Vol 234 (2) ◽  
pp. 347-357
Author(s):  
Jing Liu ◽  
Shizhao Ding ◽  
Linfeng Wang ◽  
Hongwu Li ◽  
Jin Xu
Keyword(s):  
Contact Stiffness ◽  
Planetary Gear ◽  
Gear Ratio ◽  
Gear System ◽  
Double Row ◽  
External Torque ◽  
Bearing Clearance ◽  
Gear Systems ◽  
Planetary Gear System ◽  
Stiffness And Damping

The bearing clearance, external torque, and input speed can greatly affect vibrations of the planetary gear system. The double-row planetary gear systems are commonly used in the gearbox of special vehicles, which are the key parts to obtain a larger gear ratio. Although many works have been presented to study those factors on vibrations of the single-row planetary gear system, a few works were focused on vibrations of the double-row planetary gear system with the bearing clearance. To overcome this problem, a multi-body dynamic model of a double-row planetary gear system with six planet bearings and one supported bearing of the sun gear is presented. This model is the main part of a gear box transmission system. The new model is developed for studying the effect of the bearing clearance on the planetary system. The meshing stiffness and damping between the gears are obtained by current methods in the listed references, as well as the contact stiffness and damping in bearings. The liner stiffness and damping model is used. The effects of the bearing clearance, external torque, and input speed on vibrations of the system are analyzed. The results show that vibrations of the ring gear and sun gear decrease with the increment of the external torque and increase with the increment of the input speed. Moreover, a reasonable bearing clearance can be helpful for reducing system vibrations for some mating external torque and input speed conditions. The results can provide some guidance to find new method to reduce vibrations and increase the service life of planetary gear systems.

Liapunov Stability Analysis of Elastic Shaft-Rigid Disk-Bearing Systems

1992 ◽  
Vol 59 (4) ◽  
pp. 946-954
Author(s):  
H.-Y. Huang ◽  
A. L. Schlack
Keyword(s):  
Direct Method ◽  
Rotating Shaft ◽  
Rigid Disk ◽  
Elastic Shaft ◽  
Coupling Stiffness ◽  
Modal Term ◽  
Direct Stiffness ◽  
Instability Regions ◽  
Arbitrary Location ◽  
Stiffness And Damping

A general method of analysis based on Liapunov’s direct method is presented for studying the dynamic stability of elastic shaft-rigid disk-bearing systems. A model comprised of a rigid disk rigidly attached at an arbitrary location along a flexible, rotating shaft which is mounted on two eight-component end bearings is used to develop stability criteria involving system stiffness and damping parameters. It is quantitatively shown by means of graphs for typical cases how the instability regions are reduced by (a) increasing the shaft dimensionless stiffness parameters, (b) increasing the bearing direct stiffness and damping parameters, (c) decreasing the bearing cross-coupling stiffness and damping parameters, (d) decreasing the mass ratio of the disk, and (e) increasing the disk’s radius ratio. These graphs present typical examples of the types of design information available to engineers through the equations provided in this paper. These graphs also verify that a two-modal term (N = 2) expansion is normally adequate to model the system deformations since the curves are not significantly altered by adding another term (N = 3) to the expansion. The critical value of the shaft dimensionless stiffness parameters is also studied.

scholarly journals A valid method of gas foil bearing parameter estimation: A model anchored on experimental data

2016 ◽  
Vol 232 (24) ◽  
pp. 4510-4527 ◽  
Author(s):  
Robert Hoffmann ◽  
Oliver Munz ◽  
Tomasz Pronobis ◽  
Enrico Barth ◽  
Robert Liebich
Keyword(s):  
Experimental Data ◽  
Dynamic Stiffness ◽  
Linear Structure ◽  
Order Equation ◽  
Design Stage ◽  
Frictional Contacts ◽  
Foil Bearing ◽  
Non Linear ◽  
Stiffness And Damping ◽  
The Impact

Gas foil bearings are a smart green technology and suitable for the next generation of small turbo machinery e.g. turbochargers, micro gas turbines, range extenders and compressors of fuel cells. A combination of low power loss, high speed operation and the omission of an oil system are the major advantages. To enable access to this technology, it is essential to evaluate critical speeds and onset speeds of subharmonic vibration of the rotor system in the first design stage. Hence, robust and valid models are necessary, which correctly describe the fluid structure interaction between the lubrication film and the elastic bearing structure. In the past three decades several experimental and numerical investigations of bearing parameters have been published. But the number of sophisticated models is small and there is still a lack of validation towards experimental works. To make it easy for designers dealing with this issue, the bearing parameters are often linearised about certain operating points. In this paper a method for calculating linearised bearing parameters (stiffness and damping) of gas foil bearing is presented. Experimental data are used for validation of the model. The linearised stiffness and damping values are calculated using a perturbation method. The pressure field is coupled with a two-dimensional plate model, while the non-linear bump structure is simplified by a link-spring model. It includes Coulomb friction effects inside the elastic corrugated structure and captures the interaction between the single bumps. For solving the separated perturbed Reynolds equation a static stiffness is used for the 0. order equation (stationary case) and a dynamic stiffness is applied for 1. order equation (dynamic case). Therefore, an additional dynamic structural model is applied to calculate the dynamic stiffness. The results depend on the load level and friction state of each bump. Different case studies including the impact of clearance, frictional contacts and the comparison of a linear and non-linear structure are carried out for infinitesimal perturbations. The results show, that the linear structure underestimates main and cross-coupling effects. The impact of the clearance is notable, while the impact of the overall frictional contacts is small due to relatively small loadings. The infinitely small perturbation model is adapted to the experimental setup by using a superposition of two resulting bearing parameters identifications of two total loadings including shaker forces. Due to this adaptation a good correlation with the experimental results of the bearing parameters is achieved.

scholarly journals Impact of configuration errors on the dynamic oscillation absorbers effectiveness of different masses on the seismic resistance of bridges

2019 ◽  
Vol 97 ◽  
pp. 03017
Author(s):  
Ulugbek Shermuxamedov ◽  
Said Shaumarov
Keyword(s):  
Seismic Resistance ◽  
Optimal Parameters ◽  
Main Mass ◽  
Dynamic Damping ◽  
Stiffness And Damping ◽  
The Impact

Analyzes existing known solutions for dynamic damping oscillations of bridges in earthquakes. Substantiates the impact of errors settings the two-mass systems on the efficiency of dynamic dampers of different masses (small, large and commensurate). Based on the obtained of optimal parameters were built isolines depending reduce the displacement of the main mass of the setting on the stiffness and damping for different masses. The estimates obtained allow to simplify essentially the task of designing seismic devices for bridges.

Damping of vibration of the car suspension at resonance

2021 ◽  
pp. 3-8
Author(s):  
Keyword(s):  
Mathematical Model ◽  
Block Diagram ◽  
Vibration Absorber ◽  
Optimal Parameters ◽  
Dynamic Vibration Absorber ◽  
Vibration Absorption ◽  
Dynamic Vibration ◽  
Car Suspension ◽  
Dynamic Damping ◽  
Dynamic Absorber

A block diagram of the device has been developed, which is based on the principle of dynamic vibration absorption. The design of a dynamic absorber of car suspension vibrations is considered. A mathematical model of a car suspension with a dynamic vibration absorber and the results of its numerical simulation are presented. The analysis of the results obtained makes it possible to determine the optimal parameters of the device for a dynamic vibration absorber. Keywords: suspension, car, dynamic, damping, vibration, mathematical, model, analysis, parameters

Nonlinear Modeling and Experimental Validation of Tire Nonuniformity Induced Tangential Steering Wheel Vibrations

2006 ◽  
Author(s):  
Virgile Ayglon ◽  
Nader Jalili ◽  
Imtiaz Haque
Keyword(s):  
Degrees Of Freedom ◽  
Nonlinear Modeling ◽  
Equations Of Motion ◽  
Quantitative Measure ◽  
Steering System ◽  
Steering Wheel ◽  
Vehicle Speed ◽  
Pinion Gear ◽  
Stiffness And Damping ◽  
Vehicle Chassis

This paper describes the model integration and validation that followed the development of nonlinear models of a tire with non-uniformities, a double wishbone suspension and rack-and-pinion power steering. These submodels are integrated to investigate the effects of variation of tire, suspension and steering parameters on the transmission of tire forces acting on the wheel spindle to the steering system and vehicle chassis. The tire model is based on a rigid ring model which includes mass imbalance and balancing mass. The suspension is idealized as rigid links with seven degrees-of-freedom and the bushings are represented by spring-damper elements. The equations of motion are derived using the Lagrange multiplier method in Maple, and solved numerically using Matlab DAE solver. The steering system is idealized as a four degree-of-freedom system and considers motion of the rack, rack housing, pinion gear and steering wheel. Nonlinear compliant friction is considered between the pinion gear / rack, and the steering column / chassis interfaces. The analytical model is used to develop a quantitative measure of the relative importance of the parameters such as mass/inertia, suspension bushing stiffness and damping, torsion bar stiffness and damping, rack friction and damping, to the force transmissibility to the vehicle chassis and the steering system. Experimental results include a modal analysis, a shop-testing and road testing, which are used to cross verify the numerical simulations. The testing shows the variation of forces in the steering system due to tire imbalances, emphasizing the nonlinear variation of the nibble phenomenon with vehicle speed and tire imbalance. Results obtained from simulation matches well with the experimental measurements.

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