Study on the mesh stiffness and nonlinear dynamics accounting for centrifugal effect of high-speed spur gears

2022 ◽  
Vol 170 ◽  
pp. 104686
Author(s):  
Xingyuan Zheng ◽  
Wenjun Luo ◽  
Yumei Hu ◽  
Zao He ◽  
Sheng Wang
Keyword(s):  
Nonlinear Dynamics ◽  
High Speed ◽  
Spur Gears ◽  
Mesh Stiffness ◽  
Centrifugal Effect

The influence of tooth pitting on the mesh stiffness of a pair of external spur gears

2016 ◽  
Vol 106 ◽  
pp. 1-15 ◽  
Author(s):  
Xihui Liang ◽  
Hongsheng Zhang ◽  
Libin Liu ◽  
Ming J. Zuo
Keyword(s):  
Spur Gears ◽  
Mesh Stiffness

Nonlinear dynamics of a spur gear pair with tooth root crack based on an amplitude modulation function

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Nan Gao ◽  
Shiyu Wang ◽  
Muhammad Asad Ur Rehman Bajwa
Keyword(s):  
Nonlinear Dynamics ◽  
Amplitude Modulation ◽  
Spur Gear ◽  
Dynamic Mesh ◽  
Gear Pair ◽  
Mesh Stiffness ◽  
Chaotic Motions ◽  
Content Type ◽  
Modulation Function ◽  
Nonlinear Behaviors

PurposeGear transmissions are widely utilized in practice. This paper aims to uncouple the crack feature from the cracked time-varying mesh stiffness (TVMS) and investigate the effects of the crack on the nonlinear dynamics of a spur gear pair.Design/methodology/approachAn approximate method to simulate the cracked TVMS is proposed by using an amplitude modulation function. The ratio of mesh stiffness loss is introduced to estimate the TVMS with different crack depths and angles. The dynamic responses are obtained by solving a torsional model which takes the non-loaded static transmission error, the backlash and the cracked TVMS into account. By using the bifurcation diagram, the largest Lyapunov exponent (LLE) and dynamic mesh force, the influences of crack on nonlinear behaviors are examined. The dynamic characteristics are identified from the phase diagram, Poincaré map, dynamic mesh force, time series and FFT spectra.FindingsThe comparison between the healthy and cracked gear pairs indicates that the crack affects the system motions, such as the obvious changes of impact force and unpredictable instability. Besides, the additive and difference combination frequencies can be found in periodic-1 and -2 motions, but they are covered in periodic-3 and chaotic motions. Deeper crack is an important determinant of the nonlinear behaviors at a higher speed.Originality/valueThe research provides an interesting perspective on cracked TVMS and reveals the connection between crack and nonlinear behaviors of the gear pairs.

Low excitation spur gears with variable tip diameter

2021 ◽  
Vol 263 (5) ◽  
pp. 1275-1285
Author(s):  
Joshua Götz ◽  
Sebastian Sepp ◽  
Michael Otto ◽  
Karsten Stahl
Keyword(s):  
Transmission Error ◽  
Spur Gear ◽  
Low Noise ◽  
Spur Gears ◽  
Mesh Stiffness ◽  
Helical Gears ◽  
Axial Forces ◽  
Tooth Width ◽  
Drive Trains ◽  
Static Transmission Error

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.

Coupled Dynamic and Vibration Analysis of Beveloid Geared System

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.

The torsional stiffness of involute spur gears

2004 ◽  
Vol 218 (1) ◽  
pp. 131-142 ◽  
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.

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.

Pumping Loss of Shrouded Meshed Spur Gears

2020 ◽  
Vol 142 (11) ◽  
Author(s):  
Michael J. Hurrell ◽  
Jerzy T. Sawicki
Keyword(s):  
High Speed ◽  
Spur Gear ◽  
Test Facility ◽  
Spur Gears ◽  
Cfd Analysis ◽  
Total Load ◽  
New Approach ◽  
Computational Fluid Dynamics Cfd ◽  
Loss Component ◽  
Swept Volume

Abstract High speed rotorcraft transmissions are subject to load-independent power losses consisting of drag loss and pumping loss. Tightly conforming shrouds enclosing the transmission gears are often incorporated to reduce the drag component of the total load-independent losses. However, tightly conforming axial shrouds can result in an increase in the pumping loss component. Quantifying the pumping loss of shrouded gear transmissions has been the subject of many studies. This study presents a new approach for estimating pumping loss based on the concept of swept volume and examines the applicability of the approach to various shroud configurations. The drag loss and pumping loss of a shrouded spur gear pair have been determined through testing using the NASA Glenn Research Center (GRC) Gear Windage Test Facility. The results from this testing have been compared to theoretical results using the formulations presented in this study. In addition, computational fluid dynamics (CFD) analysis has been conducted for the various shroud configurations tested at NASA GRC. The results from the CFD analysis confirm the theoretical and empirical results and provide insight into the applicability of the swept volume approach for estimating pumping power loss of shrouded gear transmissions.

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

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.

Finish Roll Forming of Spur Gears for High Efficiency

2000 ◽  
Author(s):  
Seizo Uematsu ◽  
Masana Kato
Keyword(s):  
Plastic Deformation ◽  
High Speed ◽  
High Efficiency ◽  
Tooth Profile ◽  
Roll Forming ◽  
Spur Gears ◽  
Design Data ◽  
Constant Center ◽  
The Relationship ◽  
Center Distance

Abstract Finish roll forming under the constant center distance by forced feed of tool can be conceived as a method of eliminating errors in conventional form rolling under constant loads. This method generates a high-precision tooth profile by low-speed form rolling when a high rigid screw or cam is used as loading parts. In this study, the high-speed rolling conditions of this method for necessary to be applied in practical situations are discussed. The following conclusions are obtained. When the following design data are given (module, number of teeth, addendum modification coefficient, prescribed design precision, and material characteristics), the accuracy of rolled gear can be predicted from the relationship between the required feed for the tool and the theoretically calculated plastic deformation on the tooth profile. These conclusions are verified experimentally. For example, the tooth accuracy of rolled gears with module 5 can improve from JIS class 3 to JIS class 0 or 1 when the load Fmax is 4 to 5kN and the pitch line velocity is 7 m/min.

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