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.

A Study on the Correlation Between Dynamic Transmission Error and Dynamic Tooth Loads in Spur and Helical Gears

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
N. Sainte-Marie ◽  
P. Velex ◽  
G. Roulois ◽  
J. Caillet
Keyword(s):  
Experimental Evidence ◽  
Three Dimensional ◽  
Transmission Error ◽  
System Behavior ◽  
Helical Gears ◽  
Transmission Errors ◽  
Linear Dependency ◽  
Lumped Parameter ◽  
Excitation Model ◽  
The Relationship

A three-dimensional (3D) dynamic gear model is presented which combines classic shaft, lumped parameter, and specific two-node gear elements. The mesh excitation model is based on transmission errors (TEs), and its mathematical grounding is briefly described. The validity of the proposed methodology is assessed for both spur and helical gears by comparison with experimental evidence. The model is then employed to analyze the relationship between dynamic transmission errors (DTE) and dynamic tooth loads (DF) or root stresses. It is shown that a linear dependency can be found as long as the system behavior is dominated by shaft torsion but that this linear relationship tends to disappear when bending cannot be neglected.

Effects of Belt Flexural Rigidity on the Transmission Error of a Carriage-driving System

2000 ◽  
Vol 122 (2) ◽  
pp. 213-218 ◽  
Author(s):  
Hung-Ming Tai ◽  
Cheng-Kuo Sung
Keyword(s):  
Boundary Conditions ◽  
Numerical Method ◽  
Experimental Technique ◽  
Moving Boundary ◽  
Flexural Rigidity ◽  
Three Dimensional ◽  
Transmission Error ◽  
Beam Model ◽  
Driving System ◽  
The Relationship

This paper investigates the effects of belt flexural rigidity and belt tension on transmission error of a carriage-driving system. The beam model associated with both the clamped and moving boundary conditions at two ends is utilized to derive the governing equation of the belt. The belt flexural rigidity is obtained and verified by an experimental technique. In addition, a numerical method is proposed to determine the belt profile, transmission error and transmission stiffness. Results show that transmission error of a carriage-driving system increases when the carriage moves away from the driving pulley due to finite belt flexural rigidity. According to the analyses, application of appropriate tension on the belt can significantly reduce the error. Furthermore, the transmission stiffness for representing the entire rigidity between the carriage and pulley is investigated based on the proposed beam model. A three-dimensional plot that indicates the relationship among the transmission stiffness, belt tension and the position of the carriage is obtained. [S1050-0472(00)01102-8]

Effects of Belt Flexural Rigidity on the Transmission Error of a Carriage-Driving System

2000 ◽  
Author(s):  
Hung-Ming Tai ◽  
Cheng-Kuo Sung
Keyword(s):  
Boundary Conditions ◽  
Numerical Method ◽  
Experimental Technique ◽  
Moving Boundary ◽  
Flexural Rigidity ◽  
Three Dimensional ◽  
Transmission Error ◽  
Beam Model ◽  
Driving System ◽  
The Relationship

Abstract This paper investigates the effects of belt flexural rigidity and belt tension on transmission error of a carriage-driving system. The beam model associated with both the clamped and moving boundary conditions at two ends is utilized to derive the governing equation of the belt. The belt flexural rigidity is obtained and verified by an experimental technique. In addition, a numerical method is proposed to determine the belt profile, transmission error and transmission stiffness. Results show that transmission error of a carriage-driving system increases when the carriage moves away from the driving pulley due to finite belt flexural rigidity. According to the analyses, application of appropriate tension on the belt can significantly reduce the error. Furthermore, the transmission stiffness for representing the entire rigidity between the carriage and pulley is investigated based on the proposed beam model. A three-dimensional plot that indicates the relationship among the transmission stiffness, belt tension and the position of the carriage is obtained.

Gear Dynamic Transmission Error Testing

2013 ◽  
Vol 871 ◽  
pp. 352-357
Author(s):  
Dun Cai Lei ◽  
Jin Yuan Tang ◽  
Jian Jie Tang
Keyword(s):  
Software Design ◽  
High Speed ◽  
Transmission Error ◽  
Measuring Device ◽  
Labview Software ◽  
Transmission Errors ◽  
Dynamic Transmission Error ◽  
New Type ◽  
Error Testing ◽  
Easy Operation

A measuring device for gear dynamic transmission error test is developed based on NI Labview software, and a new type eccentric bushing structure that can simulate a variety of installation errors is presented. The hardware and software design of the gear dynamic transmission error measuring device is given, and the gear dynamic transmission errors for low-speed and high-speed in different loads are gotten based on the device and the measured data. Experimental dynamic transmission error results show that the gear dynamic transmission error measuring device is a stable and friendly interface with easy operation and high accuracy, able to do real-time detection and data acquisition for gearing.

Design System for Composite Transmission Error Prediction for Automatic Transmissions

2004 ◽  
Author(s):  
Sameer Gudal ◽  
Yong Pan ◽  
Shuh-Yuan Liou ◽  
V. Sundararajan ◽  
Daniel Antonetti ◽  
...  
Keyword(s):  
Transmission Error ◽  
Transmission System ◽  
Design System ◽  
Speed Ratio ◽  
Single Pair ◽  
Contributing Factors ◽  
Transmission Errors ◽  
Automatic Transmissions ◽  
The Individual ◽  
The Relationship

Noise in vehicular automatic transmissions is a complex phenomenon involving several interacting factors. One of the contributing factors to noise for a single pair of meshing gears has been shown to be the transmission error. The transmission error (TE) is defined in terms of deviation of the speed ratio from the ideal speed ratio. It has since been hypothesized that the composite transmission error in a planetary system would be the key contributor to noise in automatic transmissions. This composite error would have to include the contributions from individual meshes and account for the configuration of the transmission system. This paper describes a design system that enables engineers to predict and study effects of parameter variation on the composite transmission error. The designer first specifies the configuration of the transmission using canonical graphs. The graph contains the elements such as gears, clutches and brakes of the transmission system as its nodes and the relationship among them for the edges. The design system uses the graph to solve for the speeds and torques. The transmission errors for the individual meshes are computed and then combined into the composite transmission error using a simple average.

Effect of Involute Contact Ratio on Spur Gear Dynamics

1999 ◽  
Vol 121 (1) ◽  
pp. 112-118 ◽  
Author(s):  
A. Kahraman ◽  
G. W. Blankenship
Keyword(s):  
Transmission Error ◽  
Spur Gear ◽  
Design Guidelines ◽  
Forced Response ◽  
Contact Ratio ◽  
Test Rig ◽  
Response Curves ◽  
Gear Mesh ◽  
Dynamic Transmission Error ◽  
Selection Of

The influence of involute contact ratio on the torsional vibration behavior of a spur gear pair is investigated experimentally by measuring the dynamic transmission error of several gear pairs using a specially designed gear test rig. Measured forced response curves are presented, and harmonic amplitudes of dynamic transmission error are compared above and below gear mesh resonances for both unmodified and modified gears having various involute contact ratio values. The influence of involute contact ratio on dynamic transmission error is quantified and a set of generalized, experimentally validated design guidelines for the proper selection of involute contact ratio to achieve quite gear systems is presented. A simplified analytical model is also proposed which accurately describes the effects of involute contact ratio on dynamic transmission error.

Finite Element/Contact Mechanics Analysis of Spur Gear Pairs With Tooth Root Cracks

2021 ◽  
Author(s):  
Yaosen Wang ◽  
Adrian A. Hood ◽  
Christopher G. Cooley
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
Contact Mechanics ◽  
Transmission Error ◽  
Spur Gear ◽  
Tooth Root ◽  
Transmission Errors ◽  
Wide Range ◽  
Dynamic Transmission Error ◽  
Root Crack

Abstract This study analyzes the nonlinear static and dynamic response in spur gear pairs with tooth root crack damage. A finite element/contact mechanics (FE/CM) model is used that accurately captures the elastic deformations on the gear teeth due to kinematic motion, tooth and rim deformations, vibration, and localized increases in compliance due to a tooth root crack. The damage is modeled by releasing the connectivity of the finite element mesh at select nodes near a tooth crack. The sensitivity of the calculated static transmission errors and tooth mesh stiffnesses is determined for varying crack initial locations, final locations, and the path from the initial to final location. Gear tooth mesh stiffness is calculated for a wide range of tooth root crack lengths, including large cracks that extend through nearly all of the tooth. Mesh stiffnesses are meaningfully reduced due to tooth root crack damage. The dynamic response is calculated for cracks of varying length. Larger cracks result in increased peak dynamic transmission errors. For small tooth root cracks the spectrum of dynamic transmission error contains components near the natural frequency of the gear pair. The spectrum of dynamic transmission error has broadband frequency response for large tooth root cracks that extend further than one-half of the tooth’s thickness.

A Frequency Domain Finite Element Approach for Three-Dimensional Gear Dynamics

2009 ◽  
Author(s):  
Christopher G. Cooley ◽  
Robert G. Parker ◽  
Sandeep M. Vijayakar
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
Frequency Domain ◽  
Dynamic Models ◽  
Three Dimensional ◽  
Transmission Error ◽  
System Level ◽  
Element Formulation ◽  
Lumped Parameter ◽  
Static Transmission Error

A finite element formulation for the dynamic response of gear pairs is proposed. Following an established approach in lumped parameter gear dynamic models, the static transmission error is used as the excitation in a frequency domain solution of the finite element vibration model. The nonlinear finite element/contact mechanics formulation provides superior calculation of static transmission error and average mesh stiffness that is used in the dynamic simulation. The frequency domain finite element calculation of dynamic response correlates to numerically integrated (time domain) finite element dynamic results and previously published experimental results. Simulation time with the proposed formulation is two orders of magnitude lower than numerically integrated dynamic results. This formulation admits system level dynamic gearbox response, which may include multiple gear meshes, flexible shafts, rolling element bearings, and housing structures.

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