Computation of dynamic transmission error for gear transmission systems using modal decomposition and Fourier series

2021 ◽  
Author(s):  
Eddy Abboud ◽  
Aurélien Grolet ◽  
Hervé Mahé ◽  
Olivier Thomas
Keyword(s):  
Fourier Series ◽  
Transmission Error ◽  
Gear Transmission ◽  
Transmission Systems ◽  
Modal Decomposition ◽  
Dynamic Transmission Error

Gear transmission error outside the normal path of contact due to corner and top contact

1999 ◽  
Vol 213 (4) ◽  
pp. 389-400 ◽  
Author(s):  
R. G. Munro ◽  
L Morrish ◽  
D Palmer
Keyword(s):  
Dynamic Test ◽  
Theoretical Models ◽  
Transmission Error ◽  
Helical Gear ◽  
Gear Transmission ◽  
The Novel ◽  
Transmission Systems ◽  
Helical Gears ◽  
Tooth Stiffness ◽  
Top Contact

This paper is devoted to a phenomenon known as corner contact, or contact outside the normal path of contact, which can occur in spur and helical gear transmission systems under certain conditions. In this case, a change in position of the driven gear with respect to its theoretical position takes place, thus inducing a transmission error referred to here as the transmission error outside the normal path of contact (TEo.p.c). The paper deals with spur gears only, but the results are directly applicable to helical gears. It systematizes previous knowledge on this subject, suggests some further developments of the theory and introduces the novel phenomenon of top contact. The theoretical results are compared with experimental measurements using a single flank tester and a back-to-back dynamic test rig for spur and helical gears, and they are in good agreement. Convenient approximate equations for calculation of TEo.p.c suggested here are important for analysis of experimental data collected in the form of Harris maps. This will make possible the calculation of tooth stiffness values needed for use in theoretical models for spur and helical gear transmission systems.

The Dynamic Transmission Error and the Tooth Meshing Force Based on ANSYS/LS-DYNA

2007 ◽  
Author(s):  
Siyu Chen ◽  
Jinyuan Tang ◽  
Xin Liu
Keyword(s):  
Dynamic Models ◽  
Gear Tooth ◽  
Deformable Body ◽  
Transmission Error ◽  
Gear Transmission ◽  
Dynamic Phenomenon ◽  
Discrete Parameter ◽  
Body Model ◽  
Wide Range ◽  
Dynamic Transmission Error

Two dynamic models of meshing contact in gear transmission are established. The transient dynamic characteristics of the gear transmission along line of action were analyzed based on deformable-body model and discrete parameter model. The curves on the displacement, the speed and the meshing force of the gear tooth meshing node with the change of time were gotten. Dynamic transmission error curves and teeth loads were computed within a wide range of rotational speed for different torques and working conditions with and without friction force. The results of the dynamic transmission error and dynamic teeth loads are validated by comparing the calculating results with that of the former experimental data. The research provides basic data for analyzing the gear impact and predicting the fatigue life of gear tooth, and it is also beneficial for the optimum design of gear parameters and the understanding of the dynamic phenomenon of gear meshing impact.

Dynamic Analysis of Gear–Shaft–Bearing Coupled System Considering Bearing Waviness Defect

2019 ◽  
Vol 15 (1) ◽  
Author(s):  
Huan Bai ◽  
Chaosheng Song ◽  
Caichao Zhu ◽  
Jianjun Tan ◽  
Xinzi Li
Keyword(s):  
Dynamic Response ◽  
Vibrational Energy ◽  
Coupled Model ◽  
Coupled System ◽  
Transmission Error ◽  
Transmission System ◽  
Gear Transmission ◽  
Dynamic Mesh ◽  
Gear Transmission System ◽  
Dynamic Transmission Error

Abstract Using finite element and lumped parameter methods, a gear–shaft–bearing coupled vibration model was developed for a single-stage gear transmission system considering bearing waviness, bearing clearance, time-varying transmission error excitation, and shaft flexibility. Runge–Kutta algorithm was applied for solving the dynamic response of the coupled model. The influences of rotational speed, the number, and amplitude of bearing waviness on the dynamics were studied. Results show that any change in the number of bearing waviness has an obvious impact on the dominant frequency component of the dynamic transmission error. When the number of bearing waviness is equal to the number or multiples of the rolling element, the dynamic mesh force occurs peak response and the system vibrates violently. At low and medium speeds range, the gear transmission system with bearing waviness has larger vibrational energy than the gear transmission system without bearing waviness, leading to unstable dynamic response, which would potentially cause a significant chaotic response. The dominant frequencies of the dynamic transmission error for the gear transmission system with bearing waviness are the ball passage frequency (BPF) and its harmonic frequency. At high speeds range, the main excitation is the transmission error both for the gear transmission systems with and without bearing waviness. In addition, the increasing amplitude of bearing waviness would enlarge the dynamic mesh force and decrease the number of loaded rolling elements.

Influence of the backlash generated by tooth accumulated wear on dynamic behavior of compound planetary gear set

2016 ◽  
Vol 231 (11) ◽  
pp. 2025-2041 ◽  
Author(s):  
Shijing Wu ◽  
Haibo Zhang ◽  
Xiaosun Wang ◽  
Zeming Peng ◽  
Kangkang Yang ◽  
...  
Keyword(s):  
Dynamic Response ◽  
Dynamic Model ◽  
Dynamic Behavior ◽  
Planetary Gear ◽  
Tooth Wear ◽  
Transmission Error ◽  
Gear Transmission ◽  
Tooth Surface ◽  
Contact Ratio ◽  
The Impact

Backlash is a key internal excitation on the dynamic response of planetary gear transmission. After the gear transmission running for a long time under load torque, due to tooth wear accumulation, the backlash between the tooth surface of two mating gears increases, which results in a larger and irregular backlash. However, the increasing backlash generated by tooth accumulated wear is generally neglected in lots of dynamics analysis for epicyclic gear trains. In order to investigate the impact of backlash generated by tooth accumulated wear on dynamic behavior of compound planetary gear set, in this work, first a static tooth surface wear prediction model is incorporated with a dynamic iteration methodology to get the increasing backlash generated by tooth accumulated wear for one pair of mating teeth under the condition that contact ratio equals to one. Then in order to introduce the tooth accumulated wear into dynamic model of compound planetary gear set, the backlash excitation generated by tooth accumulated wear for each meshing pair in compound planetary gear set is given under the condition that contact ratio equals to one and does not equal to one. Last, in order to investigate the impact of the increasing backlash generated by tooth accumulated wear on dynamic response of compound planetary gear set, a nonlinear lumped-parameter dynamic model of compound planetary gear set is employed to describe the dynamic relationships of gear transmission under the internal excitations generated by worn profile, meshing stiffness, transmission error, and backlash. The results indicate that the introduction of the increasing backlash generated by tooth accumulated wear makes a significant influence on the bifurcation and chaotic characteristics, dynamic response in time domain, and load sharing behavior of compound planetary gear set.

A Proposed Model for Stochastic Vibration Analysis of Gear Transmission Systems

1996 ◽  
Author(s):  
Y. Wang ◽  
W. Zhang
Keyword(s):  
Vibration Analysis ◽  
Linear Time ◽  
Simulation System ◽  
Gear Transmission ◽  
Random Component ◽  
Transmission Systems ◽  
Transmission Errors ◽  
Proposed Model ◽  
Rotational Vibration ◽  
Random Components

Abstract A new mathematical model is presented for analyzing the vibration of gear transmission systems with consideration of the influence of the time-variant stiffness, loads, gear transmission errors. The gear transmission system is modeled as a non-linear, time-correlated and stationary stochastic system. The transmission errors of gears are decomposed into harmonic and random components in terms of the different characteristics of their spectrums. The random component is simulated by a second order Markov process. A simulation system for vibration analysis of gear transmission systems is then developed, based on this new model. The input to this system is a Guassian white noise process and harmonic errors, and the output is the rotational vibration acceleration of gears. Some experiments are conducted to verify the proposed model. By comparing the results generated from the simulation system with those from the experiments, the proposed model is found to reach a fairly good accuracy, and thus the model is useful in designing gear transmission systems with the objective to reduce the vibration and noise of the systems in operation.

A Comparison of Analytical Predictions With Experimental Measurements of Transmission Error of Misaligned Loaded Gears

1992 ◽  
Author(s):  
Harsh Vinayak ◽  
Donald R. Houser
Keyword(s):  
Experimental Data ◽  
Load Distribution ◽  
Theoretical Calculations ◽  
Data Acquisition System ◽  
Transmission Error ◽  
Test Facility ◽  
Experimental Measurements ◽  
Gear Pair ◽  
Prediction Program ◽  
Dynamic Transmission Error

Abstract This paper deals with the experimental study of dynamic transmission error of a gear pair. Two aspects of the experiment are discussed : 1) design of the test facility and data acquisition system and 2) comparison of transmission error and load distribution with experimental data. Several gears were tested under varying misalignments. A prediction program LDP (Load distribution Program) was used for theoretical calculations of dynamic transmission error.

On the Correlation Between Dynamic Transmission Error and Dynamic Tooth Loads in Three-Dimensional Gear Systems

2015 ◽  
Author(s):  
Nina Sainte-Marie ◽  
Philippe Velex ◽  
Guillaume Roulois ◽  
Franck Marrot
Keyword(s):  
Experimental Evidence ◽  
Three Dimensional ◽  
Transmission Error ◽  
Test Rig ◽  
Transmission Errors ◽  
Linear Dependency ◽  
Lumped Parameter ◽  
Dynamic Transmission Error ◽  
Time Variations ◽  
The Relationship

A three-dimensional dynamic model is presented to simulate the dynamic behavior of single stage gears by using a combination of classic shaft, lumped parameter and specific 2-node gear elements. The mesh excitation formulation is based on transmission errors whose mathematical grounding is briefly described. The validity of the proposed methodology is assessed by comparison with experimental evidence from a test rig. The model is then employed to analyze the relationship between dynamic transmission errors and dynamic tooth loads or root stresses. It is shown that a linear dependency can be observed between the time variations of dynamic transmission error and tooth loading as long as the system can be assimilated to a torsional system but that this linear relationship tends to disappear when the influence of bending cannot be neglected.

Survey of nonlinear vibration of gear transmission systems

2003 ◽  
Vol 56 (3) ◽  
pp. 309-329 ◽  
Author(s):  
Jianjun Wang ◽  
Runfang Li and ◽  
Xianghe Peng
Keyword(s):  
Nonlinear Vibration ◽  
Review Article ◽  
Gear Transmission ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Transmission Systems ◽  
Driven Systems ◽  
The Past ◽  
Critical Issues ◽  
Basic Concepts

In this paper, the progress in nonlinear dynamics of gear driven systems in the past twenty years is reviewed, especially the gear dynamic behavior, by considering the backlash and time-varying mesh stiffness of teeth. The basic concepts, the mathematical models and the solving methods for the non-linear dynamics of geared systems are then reviewed. The critical issues for further research on the nonlinear vibration in gear transmission systems are also discussed. There are 204 references cited in this review article.

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