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.

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.

Numerical simulation of instability conditions in multiple pinion drives

2011 ◽  
Vol 225 (6) ◽  
pp. 1319-1327 ◽  
Author(s):  
K-Z Zhang ◽  
H-D Yu ◽  
X-X Zeng ◽  
X-M Lai
Keyword(s):  
Parametric Instability ◽  
Industrial Applications ◽  
Lyapunov Theory ◽  
Gear Train ◽  
Heavy Duty ◽  
Mesh Stiffness ◽  
Torque Transmission ◽  
Stiffness Variation ◽  
Parametric Instabilities ◽  
Mesh Phasing

Multiple pinion drives, parallel arrangements of the pinions for large torque transmission, are widely utilized in various heavy-duty industrial applications. For such multi-mesh gear systems, periodic mesh stiffnesses could possibly cause parametric instabilities and server vibrations. Based on the Floquet–Lyapunov theory, numerical simulations are conducted to determine the parametric instability status. For rectangular waveforms assumption of the mesh stiffness variations, the primary, secondary, and combination instabilities of the multiple pinion drives are studied. The effects of mesh stiffness parameters, including mesh frequencies, stiffness variation amplitudes, and mesh phasing, on these instabilities are yielded. Unstable regions are also indicated for different gear pair configurations. Instability conditions of three-pinion drives are obtained and compared with those of the three-stage gear train.

Parametric Instability in Planetary Gears With Frequency-Modulated Time-Varying Mesh Stiffness

2014 ◽  
Author(s):  
Xinghui Qiu ◽  
Qinkai Han ◽  
Fulei Chu
Keyword(s):  
Parametric Instability ◽  
Operating Conditions ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Rotational Model ◽  
Planetary Gears ◽  
Gear Mesh ◽  
Stiffness Variation ◽  
Speed Fluctuations ◽  
Gear Mesh Stiffness

A rotational model of planetary gears is developed which incorporates mesh stiffness variation and input speed fluctuations. Gear mesh stiffness is approximated by rectangle wave and different harmonic orders are considered. Because of speed fluctuations, the mesh stiffness is frequency modulated. The parametric instability associated with frequency-modulated time-varying stiffness is numerically investigated. The operating conditions leading to parametric instability are identified using Floquet theory and numerical integration. Whether the general laws derived for steady speed to suppress particular instabilities are applicable for fluctuating speed is verified. The effects of speed fluctuations on parametric instability are examined.

Parametric Instability of Planetary Gear Transmission Mounted on Discrete Support Struts With Minimum Ring Gear Rim Thickness Design

2018 ◽  
Author(s):  
Peng Guan ◽  
Hans DeSmidt
Keyword(s):  
Parametric Instability ◽  
Planetary Gear ◽  
Gear Transmission ◽  
Ring Gear ◽  
Mesh Stiffness ◽  
Gear Mesh ◽  
Stiffness Variation ◽  
Parametric Instabilities ◽  
Gear Mesh Stiffness ◽  
Flexible Ring

This research explores parametric instabilities of the PGT driveline system and a stability-based method for ring gear rim thickness design. Parametric excitation of a planetary gear transmission (PGT) driveline system arises from two sources: 1) gear mesh stiffness variation, 2) Interaction between moving planets, flexible ring gear and boundary struts. Many researchers have studied the parametric instability of planetary gear transmissions due to gear mesh stiffness variation, however, the effect of interaction between moving planets, flexible ring and discrete boundary struts on parametric instabilities has not been fully studied before. Especially, for sufficiently thin ring gears, this kind of effect becomes even more significant. To illustrate the novel PGT rim design proposal, firstly, a structural dynamics model of a complete PGT driveline system with elastic ring gear supported by discrete boundary struts is established. Secondly, by applying Floquet method, the parametric instability behavior due to the second parametric excitation source is fully investigated. Lastly, the design guidelines for planetary gear transmission ring gear rim thickness are proposed based on system stability from a dynamical viewpoint. The analysis and results provide new and important insights into dynamics and design of lightweight planetary gear transmission ring gear rim.

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.

Parametric Instability in a Gear Train System Due to Stiffness Variation

2013 ◽  
Author(s):  
S. Y. Wang ◽  
S. C. Sinha
Keyword(s):  
Differential Equations ◽  
Parametric Instability ◽  
Gear Train ◽  
Elastic Model ◽  
Time Varying ◽  
Ring Gear ◽  
Mesh Stiffness ◽  
Varying Coefficients ◽  
Wide Range ◽  
Stiffness Variation

The excitation from mesh stiffness variation in a tunnel gear driving system can cause excessive noise and vibrations. Since the stiffness variation may induce parametric instability, the system could be damaged on a permanent-basis. Therefore, the study of parametric instability in such system is of paramount importance. In this work, a rigid-elastic model is developed using the energy method, where the ring gear is treated as a rotating thin ring having radial and tangential deflections, whereas the pinions are assumed to be rigid bodies having translational motion relative to the radial directions of the ring gear as well as rotational motions around their centers. All gear meshes are modeled as interactions caused by time-varying springs, and the supports of the pinions are modeled as linear springs in the radial direction relative to the ring gear. The modeling leads to a set of partial-ordinary linear differential equations with time-varying coefficients. For an N planet system, the discretization process yields 2N+2 ordinary differential equations. Stability boundaries are determined using Floque’t theory for a wide range of parameter values. Specifically, the effects of mesh stiffness on the parametric instability are examined. The results show that the instability behaviors are closely related to the basic parameters when considering the time-varying excitation. This could be a serious consideration in the preliminary design of such systems.

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.

Parametric Instability in Metallic Bellows Subjected to Seismic Excitation

2010 ◽  
Author(s):  
Nobuyuki Kobayashi ◽  
Keisaku Kitada ◽  
Yoshiki Sugawara
Keyword(s):  
Parametric Instability ◽  
Fluid Pressure ◽  
Element Model ◽  
Frequency Component ◽  
Seismic Excitation ◽  
Axial Stiffness ◽  
Predominant Frequency ◽  
Earthquake Motion ◽  
Static Fluid ◽  
Stiffness Variation

This paper investigates the parametric instability of a metallic bellows filled with fluid and subjected to the variance of dynamic internal pressure due to an earthquake. The axial stiffness of the bellows varies due to the variation in internal static fluid pressure, and this stiffness variation induces a parametric instability in the bellows. A finite element model describing a bellows connected to a pipe is developed to examine the question of whether parametric instability is excited in such bellows by earthquake motion, which is not the harmonic vibration. Numerical simulations and experiments were carried out using the acceleration recorded by past recorded actual earthquakes. We find that indeed parametric instability may appear in the bellows when the natural frequency of the pipe is close to the predominant frequency component of the earthquake, though the earthquake motion is not harmonic.

Sign in / Sign up

Export Citation Format

Share Document