Vibration of High-Speed Spur Gear Webs

1998 ◽  
Vol 120 (3) ◽  
pp. 791-800 ◽  
Author(s):  
N. K. Arakere ◽  
C. Nataraj
Keyword(s):  
Weight Reduction ◽  
High Speed ◽  
High Cycle Fatigue ◽  
Equations Of Motion ◽  
Fatigue Loading ◽  
Periodic Variation ◽  
Cycle Fatigue ◽  
Periodic Excitation ◽  
Mesh Stiffness ◽  
Plane Vibration

High cycle fatigue loading of gear webs due to in-plane stresses, caused by forced excitation resulting from centrifugal loading and dynamic tooth loads, has been known to cause radial fatigue cracks. This is especially prevalent in high-speed gears used in aerospace applications, with small web thickness, for weight reduction. Radial cracks have also been observed to originate at the outer edge of lightening holes machined in gear webs for weight reduction. This paper presents an analytical treatment of the in-plane vibration of high-speed gear webs resulting from rotational effects and periodic excitation from dynamic tooth loading. Dynamic tooth loads result from the combined effect of inertia forces of gear wheels which are significant at high speeds, the periodic variation of gear mesh stiffness, and involute tooth profile errors. The gear web is modeled as a thin rotating disc and the governing differential equations of motion and the associated boundary conditions are derived from first principles. The equations are then nondimensionalized which leads to some essential nondimensional parameters. A comprehensive tooth stiffness model for spur gears is used that accounts for periodic variation of mesh stiffness. The dynamic tooth loads are obtained by solving the pertinent equations of motion, using a collocation method, that yields a closed-form expression for the periodic excitation, that is used as an input for the in-plane vibration problem. The in-plane vibration equations are solved by an approximate method of weighted residuals. It is found that the displacement fields and the resulting stresses can be significant under certain speeds and loading conditions. The interaction between the forcing frequencies due to gear teeth dynamics and the in-plane vibration natural frequencies can result in resonances that induce high fatigue stresses in the gear web. The in-plane stresses leading to high cycle fatigue loading, and frequency components of the resulting response are discussed in detail.

In-Plane Vibration of High-Speed Spur Gear Webs

1995 ◽  
Author(s):  
Nagaraj K. Arakere ◽  
C. Nataraj
Keyword(s):  
Weight Reduction ◽  
High Speed ◽  
High Cycle Fatigue ◽  
Equations Of Motion ◽  
Fatigue Loading ◽  
Periodic Variation ◽  
Cycle Fatigue ◽  
Periodic Excitation ◽  
Mesh Stiffness ◽  
Plane Vibration

Abstract High cycle fatigue loading of gear webs due to in-plane stresses, caused by forced excitation resulting from centrifugal loading and dynamic tooth loads, has been known to cause radial fatigue cracks. This is especially prevalent in high-speed gears used in aerospace applications, with small web thickness, for weight reduction. Radial cracks have also been observed to originate at the outer edge of lightening holes machined in gear webs for weight reduction. This paper presents an analytical treatment of the in-plane vibration of high-speed gear webs resulting from rotational effects and periodic excitation from dynamic tooth loading. Dynamic tooth loads result from the combined effect of inertia forces of gear wheels which are significant at high speeds, the periodic variation of gear mesh stiffness, and involute tooth profile errors. The gear web is modeled as a thin rotating disc and the governing differential equations of motion and the associated boundary conditions are derived from first principles. A comprehensive tooth stiffness model for spur gears is used that accounts for periodic variation of mesh stiffness. The dynamic tooth loads are obtained by solving the pertinent equations of motion, using a collocation method, that yields a closed-form expression for the periodic excitation, that is used as an input for the in-plane vibration problem. The in-plane vibration equations are solved by an approximate method of weighted residuals. It is found that the displacement fields and the resulting stresses can be significant under certain speeds and loading conditions. The in-plane stresses leading to high cycle fatigue loading, and frequency components of the resulting response are discussed in detail.

scholarly journals Effect of Loading Mode on Very High Cycle Fatigue Properties of High Speed Steel

2012 ◽  
Vol 78 (794) ◽  
pp. 1411-1422
Author(s):  
Yuuji SHIMATANI ◽  
Kazuaki SHIOZAWA ◽  
Sizeng LI ◽  
Hiroto YAMAMOTO ◽  
Takehiro NAKADA ◽  
...  
Keyword(s):  
High Speed ◽  
High Cycle Fatigue ◽  
High Speed Steel ◽  
Fatigue Properties ◽  
Cycle Fatigue ◽  
Loading Mode ◽  
Very High Cycle Fatigue ◽  
Very High

A Methodology for High Cycle Fatigue Characterization of Lead-Free Interconnects Under Simultaneous Harsh Environments of High Temperature and Vibration

2013 ◽  
Author(s):  
Pradeep Lall ◽  
Geeta Limaye
Keyword(s):  
High Temperature ◽  
High Speed ◽  
High Cycle Fatigue ◽  
Failure Modes ◽  
Elevated Temperatures ◽  
Natural Frequencies ◽  
Image Correlation ◽  
Lead Free ◽  
Cycle Fatigue ◽  
Increase With Increase

Current trends in the automotive industry warrant a variety of electronics for improved control, safety, efficiency and entertainment. Many of these electronic systems like engine control units, variable valve sensor, crankshaft-camshaft sensors are located under-hood. Electronics installed in under-hood applications are subjected simultaneously to mechanical vibrations and thermal loads. Typical failure modes caused by vibration induced high cycle fatigue include solder fatigue, copper trace or lead fracture. The solder interconnects accrue damage much faster when vibrated at elevated temperatures. Industry migration to lead-free solders has resulted in a proliferation of a wide variety of solder alloy compositions. Presently, the literature on mechanical behavior of lead-free alloys under simultaneous harsh environment of high-temperature vibration is sparse. In this paper, the reduction in stiffness of the PCB with temperature has been demonstrated by measuring the shift in natural frequencies. The test vehicle consisting of a variety of lead-free SAC305 daisy chain components including BGA, QFP, SOP and TSOPs has been tested to failure by subjecting it to two elevated temperatures and harmonic vibrations at the corresponding first natural frequency. The test matrix includes three test temperatures of 25C, 75C and 125C and simple harmonic vibration amplitude of 10G which are values typical in automotive testing. PCB deflection has been shown to increase with increase in temperature. The full field strain has been extracted using high speed cameras operating at 100,000 fps in conjunction with digital image correlation. Material properties of the PCB at test temperatures have been measured using tensile tests and dynamic mechanical analysis. FE simulation using global-local finite element models is thus correlated with the system characteristics such as modal shapes, natural frequencies and displacement amplitudes for every temperature. The solder level stresses have been extracted from the sub-models. Stress amplitude versus cycles to failure curves are obtained at all the three test temperatures. A comparison of failure modes for different surface mount packages at elevated test temperatures and vibration has been presented in this study.

Vibration of High-Speed Compliant Gear Pairs

2016 ◽  
Author(s):  
Christopher G. Cooley ◽  
Robert G. Parker
Keyword(s):  
High Speed ◽  
Rotation Speed ◽  
Equations Of Motion ◽  
System Structure ◽  
Vibration Modes ◽  
Mesh Stiffness ◽  
Nodal Diameter ◽  
Gear Teeth ◽  
Wide Range ◽  
System Coupling

This study analytically investigates the vibration of high-speed, compliant gear pairs using a model consisting of coupled, spinning, elastic rings. The gears are elastically coupled by a space-fixed, discrete stiffness element that represents the contacting gear teeth. Hamilton’s principle is used to derive the nonlinear governing equations of motion and boundary conditions. These equations are linearized for small vibrations about the steady equilibrium due to rotation. The equations are cast in operator form, which exemplifies their gyroscopic system structure. The eigenvalue problem is discretized using Galerkin’s method. The natural frequencies and vibration modes for an example aerospace gear pair are numerically calculated for a wide-range of rotation speeds. The system coupling leads to multiple eigenvalue veering regions as the gear rotation speed varies. Highly coupled vibration modes that have meaningful deflection in the discrete mesh stiffness occur within a set frequency band. The vibration modes within this band have distinct nodal diameter components that evolve with rotation speed.

PSBs and Non-Propagation of Small Surface and Interior Cracks in Polycrystalline Copper

2013 ◽  
Vol 592-593 ◽  
pp. 777-780 ◽  
Author(s):  
Stefanie E. Stanzl-Tschegg ◽  
Bernd M. Schönbauer
Keyword(s):  
High Cycle Fatigue ◽  
Fatigue Loading ◽  
Cycle Fatigue ◽  
Lower Stress ◽  
Small Surface ◽  
Loading Method ◽  
Very High Cycle Fatigue ◽  
Small Cracks ◽  
Number Of Cycles ◽  
Very High

PSB formation and its relevance for an eventual fatigue limit of polycrystalline electrolytic copper was studied in the very-high cycle fatigue regime with the ultrasound fatigue loading method. PSBs are formed at much lower stress/strain amplitudes than reported in earlier literature, if a high enough number of cycles is applied. Fatigue fracture takes place at approximately 50% higher amplitudes than needed for PSB formation, which is likewise in contrast to former literature results. Non-propagation of small cracks, originating from intrusions or PSB-induced non-propagating grain-boundary cracks are made responsible for this different material response.

OS0706 Effect of loading mode on very high cycle fatigue properties in high-speed tool steel

2009 ◽  
Vol 2009 (0) ◽  
pp. 267-269
Author(s):  
Kazuaki SHIOZAWA ◽  
Hiroto YAMAMOTO ◽  
Yuji SHIMATANI ◽  
Takehiro NAKADA ◽  
Takashi YOSHIMOTO ◽  
...  
Keyword(s):  
Tool Steel ◽  
High Speed ◽  
High Cycle Fatigue ◽  
Fatigue Properties ◽  
Cycle Fatigue ◽  
Loading Mode ◽  
Very High Cycle Fatigue ◽  
Very High

scholarly journals Process Induced Residual Stress Effect on Fatigue Lifetime of Automotive Steel Components

2014 ◽  
Vol 996 ◽  
pp. 808-813
Author(s):  
Elias Merhy ◽  
Ngadia Taha Niane ◽  
Bastien Weber ◽  
Philippe Bristiel
Keyword(s):  
Residual Stress ◽  
Heat Affected Zone ◽  
High Cycle Fatigue ◽  
Low Cycle Fatigue ◽  
Welding Process ◽  
Fatigue Loading ◽  
Stress Effect ◽  
Cycle Fatigue ◽  
Residual Stress Field ◽  
Fatigue Lifetime

Metal Active Gas (MAG) welding process of steel sheets generates, in the vicinity of the welding joint, the well-known Heat Affected Zone (HAZ) in which the material presents more microstructural defects compared to the original metal. Since high cycle fatigue is largely dependent on the material microstructure features, the HAZ is considered as the weakest zone under high cycle fatigue loading. In addition, the welding causes, in the Heat Affected Zone, irreversible plastic strains that induce important residual stress fields in this critical zone of the structure. Therefore, in order to properly predict the high cycle fatigue life time of the welded automotive components, it is of primordial importance to first identify and then consider, if necessary, the welding induced residual stress field in the structure modeling. In this work, it is found that residual stresses have non-negligible impact on high cycle fatigue lifetime, while its effect is minor in the low cycle fatigue domain.

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