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.

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.

An Experimental Investigation of the Steady-State Response of a Noncontacting Flexibly Mounted Rotor Mechanical Face Seal

1995 ◽  
Vol 117 (1) ◽  
pp. 153-159 ◽  
Author(s):  
An Sung Lee ◽  
Itzhak Green
Keyword(s):  
Experimental Investigation ◽  
Steady State ◽  
Dynamic Behavior ◽  
Amplitude Ratio ◽  
Theoretical Work ◽  
Operating Conditions ◽  
Superior Performance ◽  
Steady State Response ◽  
State Response ◽  
Operation Conditions

Recent theoretical work on the dynamics of the noncontacting flexibly mounted rotor (FMR) seal has shown that it is superior in every aspect of dynamic behavior compared to the flexibly mounted stator (FMS) seal. The FMR seal is inherently stable regardless of the operating speed, the maximum relative misalignment response is smaller, and the critical stator misalignment is larger. All these are measures of superior performance. This work undertakes the experimental investigation of the dynamic behavior of a noncontacting FMR seal. The steady-state response of the FMR seal was measured at various operating conditions. The results are given in terms of dynamic and static transmissibilities, i.e., amplitude ratio of responses to two forcing inputs: the initial rotor and fixed stator misalignments. These are then compared to the analytical predictions. Further, operation maps are drawn for each set of operation conditions. The maps indicate how safely (away from contact) the seal operates. It is shown that the combination of the seal parameters that maximize the fluid film stiffness is optimal for safe noncontacting operation.

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.

Steady-State Response of a Piping System Under Harmonic Excitations Considering Pipe-Support Friction With Variable Normal Loads

2015 ◽  
Vol 137 (5) ◽  
Author(s):  
José Argüelles ◽  
Euro Casanova
Keyword(s):  
Steady State ◽  
Operating Conditions ◽  
Dynamic Loads ◽  
Computational Time ◽  
Piping System ◽  
Steady State Response ◽  
State Response ◽  
Harmonic Excitations ◽  
Piping Systems ◽  
Support Surfaces

Dynamic loads in piping systems are mainly caused by transient phenomena generated by operating conditions or installed equipment. In most cases, these dynamic loads may be modeled as harmonic excitations, e.g., pulsating flow. On the other hand, when designing piping systems under dynamic loads, it is a common practice to neglect strong nonlinearities such as shocks and friction between pipe and support surfaces, mainly because of the excessive cost in terms of computational time and the complexity associated with the integration of the nonlinear equations of motion. However, disregarding these nonlinearities for some systems may result in overestimated dynamic amplitudes leading to incorrect analysis and designs. This paper presents a numerical approach to calculate the steady-state response amplitudes of a piping system subjected to harmonic excitations and considering dry friction between the pipe and the support surfaces, without performing a numerical integration. The proposed approach permits the analysis of three dimensional piping systems, where the normal forces may vary in time and is based in the hybrid frequency–time domain method (HFT). Results of the proposed approach are compared and discussed with those of a full integration scheme, confirming that HFT is a valid and computationally feasible option.

Nonlinear Resonant Vibration of Counter-Shaft Gears With Fluctuating Mesh Stiffness

2009 ◽  
Author(s):  
Robert G. Parker
Keyword(s):  
Steady State ◽  
Perturbation Analysis ◽  
Numerical Solutions ◽  
Design Guidelines ◽  
Resonant Vibration ◽  
Steady State Response ◽  
Mesh Stiffness ◽  
Closed Form Solutions ◽  
System Parameters ◽  
State Response

This work studies the nonlinear, parametrically excited dynamics of counter-shaft gear systems. The dynamic model includes parametric excitations and tooth contact loss. The steady state response is found using perturbation analysis and compared against numerical solutions. The mesh interactions depend strongly on the relation of the two mesh periods. The closed-form solutions provide design guidelines in terms of the system parameters.

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