Numerical and experimental investigation of a spur gear pair with unloaded static transmission error

Purpose The purpose of this paper is to investigate the dynamic responses of a spur gear pair with unloaded static transmission error (STE) excitation numerically and experimentally and the influences of the system factors including mesh stiffness, error excitation and torque on the dynamic transmission error (DTE). Design/methodology/approach A simple lumped parameters dynamic model of a gear pair considering time-varying mesh stiffness, backlash and unloaded STE excitation is developed. The STE is calculated from the measured tooth profile deviation under the unloaded condition. A four-square gear test rig is designed to measure and analyze the DTE and vibration responses of the gear pair. The dynamic responses of the gear transmission are studied numerically and experimentally. Findings The predicted numerical DTE matches well with the experimental results. When the real unloaded STE excitation without any approximation is used, the dynamic response is dominated by the mesh frequency and its high order harmonic components, which may not be result caused by the assembling error. The sub-harmonic and super-harmonic resonant behaviors are excited because of the high order harmonic components of STE. It will not certainly prevent the separations of mesh teeth when the gear pair is under the condition of high speed and heavy load. Originality/value This study helps to improve the modeling method of the dynamic analysis of spur gear transmission and provide some reference for the understanding of the influence of mesh stiffness, STE excitation and system torque on the vibration behaviors.

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Study on Effect of Surface Friction on the Dynamic Behaviours of Cylindrical Gear Transmission

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.139-141.2316 ◽

2010 ◽

Vol 139-141 ◽

pp. 2316-2321

Author(s):

Jin Yuan Tang ◽

Qi Bo Wang ◽

Cai Wang Luo

Keyword(s):

Sudden Change ◽

Surface Friction ◽

Transmission Error ◽

Spur Gear ◽

Gear Transmission ◽

Dynamic Responses ◽

Time Varying ◽

Cylindrical Gear ◽

Static Transmission Error ◽

Effect Of Surface

The effect of surface friction on the dynamic response of spur gear pair is investigated in this paper. Firstly, surface friction during the mesh is described briefly, and realistic time-varying tooth stiffness and realistic static transmission error are introduced. Subsequently, the differential equation of the torsional vibration of gear transmission is developed in which the realistic time-varying stiffness and realistic static transmission error are incorporated. Finally, using the numerical simulation method, the solutions in time domain and spectrum graphs of the nonlinear system are obtained. Results show that surface friction has great influences on the dynamic responses nearby the pitch point but less influences far away the pitch point. Surface friction may also bring sudden change to the dynamic responses at pitch point when the rotational speed is low.

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Nonlinear dynamic response of a spur gear pair based on the modeling of periodic mesh stiffness and static transmission error

Applied Mathematical Modelling ◽

10.1016/j.apm.2019.03.026 ◽

2019 ◽

Vol 72 ◽

pp. 444-469 ◽

Cited By ~ 12

Author(s):

Yi Yang ◽

Liyan Cao ◽

Hang Li ◽

Yiping Dai

Keyword(s):

Dynamic Response ◽

Nonlinear Dynamic ◽

Transmission Error ◽

Spur Gear ◽

Gear Pair ◽

Mesh Stiffness ◽

Nonlinear Dynamic Response ◽

Static Transmission Error

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

Engineering Computations ◽

10.1108/ec-06-2020-0334 ◽

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.

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Low excitation spur gears with variable tip diameter

INTER-NOISE and NOISE-CON Congress and Conference Proceedings ◽

10.3397/in-2021-1799 ◽

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.

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Nonlinear Dynamic Characteristic Analysis of a Coated Gear Transmission System

Coatings ◽

10.3390/coatings10010039 ◽

2020 ◽

Vol 10 (1) ◽

pp. 39

Author(s):

Yangyi Xiao ◽

Liyang Fu ◽

Jing Luo ◽

Wankai Shi ◽

Minglin Kang

Keyword(s):

Dynamic Characteristic ◽

Time History ◽

Spur Gear ◽

Transmission System ◽

Gear Transmission ◽

Phase Curve ◽

Gear Pair ◽

Characteristic Analysis ◽

Mesh Stiffness ◽

Gear Transmission System

Coatings can significantly improve the load-carrying performance of a gear surface, but how they affect the vibration characteristic of the system is an urgent issue to be solved. Taking into account the nonlinear factors like the variable mesh stiffness, friction, backlash, and transmission error, a six-degree-of-freedom spur gear transmission system with coatings is presented. Meanwhile, the finite element method is applied to acquire the time-varying mesh stiffness of the coated gear pair in the engagement process. With the support of the time-history curve, phase curve, Poincare map, and fast Fourier transform spectrum, the dynamic characteristics and the effects of the coating elastic modulus on vibration behaviors of a gear transmission system are minutely dissected by using a numerical integration approach. Numerical cases illustrate that the dynamic characteristic of a gear transmission system tends toward a one-period state under the given operating condition. They also indicate that, compared with softer coatings, stiffer ones can properly enhance the transmission performance of the coated gear pair. Numerical results are also compared with previous studies, and can establish a theoretical basis for dynamic design and vibration control of the coated gear transmission system.

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Dynamic Model of Spur Gear Pair with Modulation Internal Excitation

International Journal of Rotating Machinery ◽

10.1155/2017/1264904 ◽

2017 ◽

Vol 2017 ◽

pp. 1-8 ◽

Cited By ~ 2

Author(s):

Zhong Wang ◽

Lei Zhang ◽

Yuan-Qing Luo ◽

Chang-Zheng Chen

Keyword(s):

Dynamic Model ◽

Transmission Error ◽

Spur Gear ◽

Experimental Result ◽

Time Varying ◽

Gear Pair ◽

Mesh Stiffness ◽

Gear Mesh ◽

Internal Excitation ◽

Modulation Sideband

In the actual measurements, vibration and noise spectrum of gear pair often exhibits sidebands around the gear mesh harmonic orders. In this study, a nonlinear time-varying dynamic model of spur gear pair was established to predict the modulation sidebands caused by the AM-FM modulation internal excitation. Here, backlash, modulation time-varying mesh stiffness, and modulation transmission error are considered. Then the undamped natural mode was studied. Numerical simulation was made to reveal the dynamic characteristic of a spur gear under modulation condition. The internal excitation was shown to exhibit obvious modulation sideband because of the modulation time-varying mesh stiffness and modulation transmission error. The Runge-Kutta method was used to solve the equations for analyzing the dynamic characteristics with the effect of modulation internal excitation. The result revealed that the response under modulation excitation exhibited obvious modulation sideband. The response under nonmodulation condition was also calculated for comparison. In addition, an experiment was done to verify the prediction of the modulation sidebands. The calculated result was consistent with the experimental result.

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Dynamics of a Truck Gearbox

6th International Power Transmission and Gearing Conference: Advancing Power Transmission Into the 21st Century ◽

10.1115/detc1992-0031 ◽

1992 ◽

Author(s):

J. Perret-Liaudet ◽

J. Sabot

Keyword(s):

Numerical Simulations ◽

Dynamic Behaviour ◽

Equations Of Motion ◽

Transmission Error ◽

Gear Transmission ◽

The Finite Element Method ◽

Mesh Stiffness ◽

Gear Mesh ◽

Static Transmission Error ◽

Gear Mesh Stiffness

Abstract This work is concerned with numerous numerical simulations of the overall dynamic behaviour of a parallel helical gear transmission. These results are compared to vibratory measurements made with a simplified gearbox test rig. The dynamic modeling of the elastic components of the gear transmission (gears, shafts, bearings, housing) is realized using the finite element method. Fluctuated gear mesh stiffness is introduced owing to stiffness matrix which describes the elastic coupling between the pinion and the wheel. The kinematic transmission error is introduced as a vibratory excitation source. The equations of motion are established in a truncated modal base deduced from the average characteristics of the structure. A new computing method, called “Spectral Method”, is used for analytical study of a simplified gearbox whose housing is a simple rectangular plate. The numerical results allows us to conclude on the dominent phenomenon of the overall dynamic behaviour of the gear transmission. They exhibit in particular the main characteristics of the transfer between the static transmission error and the vibratory response of the gearbox. A series of vibration measurements made on a gearbox close to that used for the numerical simulations, has confirmed this characteristics.

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Effects of directional rotation radius and transmission error on the dynamic characteristics of face gear transmission system

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

10.1177/0954406213500745 ◽

2013 ◽

Vol 228 (7) ◽

pp. 1108-1118 ◽

Cited By ~ 4

Author(s):

Jinyuan Tang ◽

Zehua Hu ◽

Siyu Chen ◽

Duncai Lei

Keyword(s):

Dynamic Characteristics ◽

Transmission Error ◽

Transmission System ◽

Gear Transmission ◽

Dynamic Factor ◽

Gear Pair ◽

Face Gear ◽

Amplitude Variation ◽

Gear Transmission System ◽

Static Transmission Error

The effects of directional rotation radius and transmission error excitation on the nonlinear dynamic characteristics of face gear transmission system are analyzed. First, the accurate time-varying mesh stiffness is calculated using finite element method, and the nonlinear motion equation of the system under static transmission error excitation is proposed. The frequency response curve, time history curve, dynamic mesh force curve and dynamic factor curve are given, and the phenomena of jump, multiple solutions and tooth impact are observed. The numerical results show that the effect of amplitude variation of directional rotation radius on the dynamic characteristics of face gear pair is less conspicuous than that of transmission error but actually existing. The amplitude of the dynamic response of face gear pair reduces to some extent with the uniform distribution of the loading area through enlarging the amplitude variation of directional rotation radius. The static transmission error excitation should be reduced to perfect the transmission property. The system is in periodic motion most of the time, and tooth impact occurs only near [Formula: see text] . Since its dynamic property at low velocity and high velocity is good, the system should get through the resonant area quickly in work.

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Dynamic Analysis of Contacting Spur Gear Pair for Fast System Simulation

Solid State Phenomena ◽

10.4028/www.scientific.net/ssp.110.151 ◽

2006 ◽

Vol 110 ◽

pp. 151-162 ◽

Cited By ~ 2

Author(s):

Daisuke Suzuki ◽

Shigeru Horiuchi ◽

Jin Hwan Choi ◽

Han Sik Ryu

Keyword(s):

System Simulation ◽

Transmission Error ◽

Spur Gear ◽

Contact Analysis ◽

Gear System ◽

Force Model ◽

Gear Pair ◽

Time Step ◽

Efficient System ◽

Static Transmission Error

The prime source of vibration and noise in a gear system is originated from transmission error between the meshing gears. In this paper, the dynamic modeling method and response of a spur gear pair for the efficient system simulation are investigated by using a detailed contact analysis at each time step. Input values such as time-varying mesh stiffness and static transmission error excitation are not required in this investigation because mesh forces are obtained by contact analysis directly. The efficient contact search kinematics and algorithms in the context of the compliant contact model are developed to detect the interactions between teeth surfaces. In this investigation the compliant force model based on the Herzian law is employed using Coulomb friction force model, and dynamic transmission error (DTE) and mesh frequency values of contacting gear system are also illustrated.

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