Effect of Teeth Friction on Transmission Errors and Tooth Load of Spur Gears

2015 ◽  
Author(s):  
Chan Il Park
Keyword(s):  
Friction Force ◽  
Sliding Friction ◽  
Primary Source ◽  
Transmission Error ◽  
Spur Gears ◽  
Mesh Stiffness ◽  
Transmission Errors ◽  
Sliding Mechanism ◽  
The Moment ◽  
The Relationship

Transmission error is typically understood to act as the primary source of gearbox noise and vibration. This paper investigates the effect of sliding friction on the transmission error and tooth load of spur gears. To do so, the kinematic relation for the sliding mechanism of spur gears and mesh stiffness was calculated. The relationship between tooth load, tooth errors and mesh compliance as well as the moment balance equation in consideration of the teeth friction force are derived. Transmission error, tooth load, and the teeth friction force of gears with/without modification were investigated. As the results, friction caused an increase in tooth load and transmission error in gear approach and a decrease in tooth load and transmission error in gear recess.

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.

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.

ENERGY DISSIPATION IN POST-TENSIONED SELF-CENTERING PRECAST CONCRETE CONNECTIONS WITH A FRICTION DEVICE

2015 ◽  
Vol 2 (1) ◽  
Author(s):  
Takeaki Koshikawa
Keyword(s):  
Energy Dissipation ◽  
Friction Force ◽  
Precast Concrete ◽  
Design Parameters ◽  
Effective Energy ◽  
Energy Dissipation Capacity ◽  
Post Tensioning ◽  
The Moment ◽  
The Relationship ◽  
Post Tensioned

This paper presents an analytical study on the energy dissipation capacity of unbonded post-tensioned self-centering precast concrete beam-column connections that have a friction device only below the beam or on the web. The energy dissipation capacity is quantified using an effective energy dissipation ratio. To quantitatively evaluate the influence of three design parameters on the energy dissipation capacity, nonlinear analyses were carried out using a section-analysis method to predict the relationship between the moment and the relative rotation at the beam-column interface under cyclic loading. The design parameters were the initial post-tensioning force in the unbonded post-tensioning tendon, the friction force, and the location of the friction device. The analysis results show that the effective energy dissipation ratios for connections whose friction devices are in the same location can be related to the ratio of the friction force to the initial post-tensioning force.

Transmission Error in Synchronous Belt With Resonance Under Installation Tension

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
Masanori Kagotani ◽  
Hiroyuki Ueda
Keyword(s):  
Transmission Error ◽  
Speed Ratio ◽  
Experimental Transmission ◽  
Transmission Errors ◽  
Belt Drives ◽  
Concave Shape ◽  
Mode Vibration ◽  
The Difference ◽  
The Moment ◽  
Good Agreement

Synchronous belt drives generate resonance on the belt spans between the driving and driven pulleys when the transverse natural frequency of the belt, matches the meshing frequency of the belt tooth and the pulley tooth. The resonance of the belt spans affects the accuracy of rotation transmission. In the present study, the mechanisms generating the transmission error in synchronous belt drives under installation tension and a pulley speed ratio of 1:1 are investigated theoretically and experimentally for the case in which the belt spans generate first mode vibration due to resonance. In addition, the change in the shaft load caused by resonance is examined. The calculated and experimental transmission errors show good agreement, and so the validity of our analysis is confirmed. Transmission error is generated by the difference in displacement between the upper and lower belt spans due to the convex or concave shape, the difference in the amount of belt climbing at the beginning and end of meshing, and the generation of torque due to the moment of inertia on the driven side. The transmission error has a period of 1/2 of one pitch of the pulley, and the generated change in the shaft load, which is the sum of the displacement due to the convex or concave shape of the upper and lower spans and the sum of the belt climbing at the beginning and end of meshing, has a period of one pitch of the pulley.

Transmission Error in Synchronous Belt With Resonance Under Installation Tension

2011 ◽  
Author(s):  
Masanori Kagotani ◽  
Hiroyuki Ueda
Keyword(s):  
Transmission Error ◽  
Speed Ratio ◽  
Experimental Transmission ◽  
Transmission Errors ◽  
Belt Drives ◽  
String Vibration ◽  
Mode Vibration ◽  
The Difference ◽  
The Moment ◽  
Good Agreement

Synchronous belt drives are widely employed to transmit rotation accurately. The belt spans between the driving and driven pulleys generate resonance when the transverse natural frequency of the belt, as in string vibration, matches the meshing frequency of the belt tooth and the pulley tooth. The resonance of the belt spans affects the behavior of the transmission error. In the present study, the mechanisms generating the transmission error in synchronous belt drives under installation tension and a pulley speed ratio of 1:1 are investigated theoretically and experimentally for the case in which the belt spans generate first mode vibration due to resonance. The calculated and experimental transmission errors show good agreement, and so the validity of our analysis is confirmed. The transmission error has a period of 1/2 of one pitch of the pulley, and is generated by the difference in displacement between the upper and lower belt spans, the difference in the amount of belt climbing at the beginning and end of meshing, and the generation of torque due to the moment of inertia on the driven side.

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.

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.

Analytical Study of Helical Gear Dynamics With Sliding Friction Using Floquet Theory

2007 ◽  
Author(s):  
Song He ◽  
Rajendra Singh
Keyword(s):  
Floquet Theory ◽  
Sliding Friction ◽  
Initial Conditions ◽  
Transmission Error ◽  
Helical Gear ◽  
Degree Of Freedom ◽  
Analytical Models ◽  
Mesh Stiffness ◽  
Forcing Function ◽  
Dynamic Transmission Error

Analytical models of a helical gear pair are developed in order to examine the effect of sliding friction on the dynamic transmission error. Simplified 6 degree-of-freedom and single degree-of-freedom analytical models are developed. These models characterize the contact plane dynamics and capture the velocity reversal at the pitch line due to sliding friction. By assuming a constant mesh stiffness density along the contact lines, a linear time-varying model (with parametric excitation) is obtained. The effect of sliding friction is quantified by an effective mesh stiffness term. Floquet theory is then used to obtain closed-form solutions to the dynamic transmission error given periodic piece-wise linear tooth stiffness function. Responses to both initial conditions and forcing function under a nominal torque are derived. Analytical models are validated by comparing predictions with numerical simulations. Finally, parametrically-induced instability issues are briefly mentioned.

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