Analytical investigation of profile shifts on the mesh stiffness and dynamic characteristics of spur gears

One important source of noise in drive trains are transmissions. In numerous applications, it is necessary to use helical instead of spur gear stages due to increased noise requirements. Besides a superior excitation behaviour, helical gears also show additional disadvantageous effects (e.g. axial forces and tilting moments), which have to be taken into account in the design process. Thus, a low noise spur gear stage could simplify design and meet the requirements of modern mechanical drive trains. The authors explore the possibility of combining the low noise properties of helical gears with the advantageous mechanical properties of spur gears by using spur gears with variable tip diameter along the tooth width. This allows the adjustment of the total length of active lines of action at the beginning and end of contact and acts as a mesh stiffness modification. For this reason, several spur gear designs are experimentally investigated and compared with regard to their excitation behaviour. The experiments are performed on a back-to-back test rig and include quasi-static transmission error measurements under load as well as dynamic torsional vibration measurements. The results show a significant improvement of the excitation behaviour for spur gears with variable tip diameter.

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Dynamic analysis of a helical geared rotor-bearing system with composite rotating shafts

Aircraft Engineering and Aerospace Technology ◽

10.1108/aeat-04-2021-0095 ◽

2021 ◽

Vol ahead-of-print (ahead-of-print) ◽

Author(s):

Ying-Chung Chen ◽

Xu Feng Cheng ◽

Siu-Tong Choi

Keyword(s):

Composite Material ◽

Dynamic Analysis ◽

Dynamic Characteristics ◽

Mesh Stiffness ◽

Content Type ◽

Gear Mesh ◽

Rotor Bearing ◽

Rotating Shafts ◽

Gear Mesh Stiffness ◽

Bearing System

Purpose This study aims to study the dynamic characteristics of a helical geared rotor-bearing system with composite material rotating shafts. Design/methodology/approach A finite element model of a helical geared rotor-bearing system with composite material rotating shafts is developed, in which the rotating shafts of the system are composed of composite material and modeled as Timoshenko beam; a rigid mass is used to represent the gear and their gyroscopic effect is taken into account; bearings are modeled as linear spring-damper; and the equations of motion are obtained by applying Lagrange’s equation. Natural frequencies, mode description, lateral responses, axial responses, lamination angles, lamination numbers, gear mesh stiffness and bearing damping coefficients are investigated. Findings The desired mechanical properties could be constructed using different lamination numbers and fiber included angles by composite rotating shafts. The frequency of the lateral module decreases as the included angle of the fibers and the principal shaft of the composite material rotating shaft increase. Because of the gear mesh stiffness increase, the resonance frequency of the coupling module of the system decreases, the lateral module is not influenced and the steady-state response decreases. The amplitude of the steady-state lateral and axial responses gradually decreases as the bearing damping coefficient increases. Practical implications The model of a helical geared rotor-bearing system with composite material rotating shafts is established in this paper. The dynamic characteristics of a helical geared rotor-bearing system with composite rotating shafts are investigated. The numerical results of this study can be used as a reference for subsequent personnel research. Originality/value The dynamic characteristics of the geared rotor-bearing system had been reported in some literature. However, the dynamic analysis of a helical geared rotor-bearing system with composite material rotating shafts is still rarely investigated. This paper shows some novel results of lateral and axial response results obtained by different lamination angles and different lamination numbers. In the future, it makes valuable contributions for further development of dynamic analysis of a helical geared rotor-bearing system with composite material rotating shafts.

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Coupled Dynamic and Vibration Analysis of Beveloid Geared System

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.215-216.917 ◽

2012 ◽

Vol 215-216 ◽

pp. 917-920

Author(s):

Rong Fan ◽

Chao Sheng Song ◽

Zhen Liu ◽

Wen Ji Liu

Keyword(s):

Transmission Error ◽

Time Varying ◽

Spur Gears ◽

Dynamic Coupling ◽

Nonlinear Dynamic Model ◽

Mesh Stiffness ◽

Hypoid Gears ◽

Helical Gears ◽

Beveloid Gears ◽

Vibration Model

Dynamic modeling of beveloid gears is less developed than that of spur gears, helical gears and hypoid gears because of their complicated meshing mechanism and 3-dimsional dynamic coupling. In this study, a nonlinear systematic coupled vibration model is created considering the time-varying mesh stiffness, time-varying transmission error, time-varying rotational radius and time-varying friction coefficient. Numerical integration applying the explicite Runge-Kutta formula and the implicit direct integration is used to solve the nonlinear dynamic model. Also, the dynamic characteristics of the marine gear system are investigated.

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The torsional stiffness of involute spur gears

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1243/095440604322787009 ◽

2004 ◽

Vol 218 (1) ◽

pp. 131-142 ◽

Cited By ~ 51

Author(s):

J Wang ◽

I Howard

Keyword(s):

Finite Element ◽

Gear Tooth ◽

Torsional Stiffness ◽

Spur Gears ◽

Adaptive Meshing ◽

Mesh Stiffness ◽

Finite Element Program ◽

Tooth Stiffness ◽

Element Program ◽

The Individual

This paper presents the results of a detailed analysis of torsional stiffness of a pair of involute spur gears in mesh using finite element methods. Adaptive meshing has been employed within a commercial finite element program to reveal the detailed behaviour in the change over region from single- to double-tooth contact zones and vice versa. Analysis of past gear tooth stiffness models is presented including single- and multitooth models of the individual and combined torsional mesh stiffness. The gear body stiffness has been shown to be a major component of the total mesh stiffness, and a revised method for predicting the combined torsional mesh stiffness is presented. It is further shown tha the mesh stiffness and load sharing ratios will be a function of applied load.

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Static and Dynamic Tooth Loading in Spur and Helical Geared Systems: Experiments and Code Validation

Volume 6: 8th International Power Transmission and Gearing Conference ◽

10.1115/detc2000/ptg-14435 ◽

2000 ◽

Author(s):

Sébastien Baud ◽

Philippe Velex

Keyword(s):

Linear Time ◽

Primary Objective ◽

Integration Scheme ◽

Spur Gears ◽

Mesh Stiffness ◽

Response Curves ◽

Time Step ◽

Contact Conditions ◽

Rotor Systems ◽

Contact Algorithm

Abstract The primary objective of this study is to validate a specific finite element code aimed at simulated dynamic tooth loading in geared rotor systems. Experiments have been conducted on a high-precision single stage spur and helical gear reducer with flexible shafts mounted on hydrostatic or hydrodynamic bearings. The numerical model is based on classical elements (shaft, lumped stiffnesses, ...) and on an original gear element which accounts for non-linear time-varying mesh stiffness, gear errors and tooth shape modifications. External and parametric excitations are derived from the instantaneous contact conditions between the mating flanks by using an iterative contact algorithm inserted in a time-step integration scheme. In a first step, experimental and numerical results at low speeds are compared and it is demonstrated that the proposed tooth mesh interface model is valid. Comparisons are then extended to dynamic fillet stresses on both spur and helical gears between 50–6000 rpm on pinion shaft. Despite a localized problem in the case of spur gears with one particular bearing arrangement, the broad agreement between the experimental and numerical response curves proves that the model is representative of the dynamic behavior of geared systems.

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