Effects of Gear Dimensions and Tooth Surface Modifications on the Loaded Transmission Error of a Helical Gear Pair

1998 ◽  
Vol 120 (1) ◽  
pp. 119-125 ◽  
Author(s):  
M. Umeyama ◽  
M. Kato ◽  
K. Inoue
Keyword(s):  
Transmission Error ◽  
Tooth Surface ◽  
Contact Ratio ◽  
Rotational Angle ◽  
Actual Contact ◽  
Transmission Errors ◽  
Effective Contact ◽  
Tooth Surfaces ◽  
Helical Gear Pair ◽  
Tooth Pair

Analysis of the loaded transmission error proved that the actual contact ratio and the effective contact ratios are the valid indices. In order to calculate the loaded transmission error, deformations of a pair of teeth are estimated using Hertzian formulas for the approach deformation and approximate formulas based on the FEM for the bending deflection. The actual contact ratio εr is defined using the rotational angle during which a tooth pair is actually in contact with each other. εr increases with the increase of applied loads. The effective contact ratio, εn, is determined geometrically by gear dimensions and modified tooth surfaces based on the path of contact. Adopting these ratios, the following characteristics are derived. 1) The loaded transmission error correlates to εr when it is smaller than εn and correlates to εn when εr exceeds εn. 2) Loaded transmission errors have their minimums and maximums at the same values of εr. 3) No load transmission error is the largest among the maximums. 4) Gear pairs with higher values of εn show lower loaded transmission error.

Observation of Ghost Noise on Ground Gears With Vibration Measurement and Detection of Surface Undulation

2000 ◽  
Author(s):  
Shigeki Matsumura ◽  
Haruo Houjoh ◽  
Shun-ichi Ohshima ◽  
Hiroaki Nagoya
Keyword(s):  
Spectrum Analysis ◽  
Transmission Error ◽  
Entropy Method ◽  
Vibration Measurement ◽  
Tooth Surface ◽  
Integer Order ◽  
Tooth Surfaces ◽  
Surface Deviation ◽  
Surface Undulation ◽  
Helical Gear Pair

Abstract In this research, we discuss about the peculiar vibration behavior of a helical gear pair that appears at non-integer order of the meshing frequency. It is supposed that the vibration is generated because of the undulation on tooth surfaces having different cycles of transmission error from tooth mesh cycle. But, it is difficult to detect the undulation with direct measurement of tooth shapes because its amplitude is very small and the length of measured tooth profile is relatively short for spectrum analysis. At first, characteristics of tooth surface undulation are discussed with spectra of measured gear vibration. It makes clear that there are integer order surface undulation components of gear rotation. Next, possibility of the spectrum analysis of measured tooth surface deviation is also discussed using Maximum Entropy Method.

Application and Investigation of Modified Helical Gears With Several Types of Geometry

2007 ◽  
Author(s):  
Ignacio Gonzalez-Perez ◽  
Alfonso Fuentes ◽  
Faydor L. Litvin ◽  
Kenichi Hayasaka ◽  
Kenji Yukishima
Keyword(s):  
Gear Tooth ◽  
Tooth Surface ◽  
Contact Ratio ◽  
Tooth Contact Analysis ◽  
Helical Gears ◽  
Transmission Errors ◽  
Advantages And Disadvantages ◽  
Bearing Contact ◽  
Tooth Surfaces ◽  
Gear Drives

Involute helical gears with modified geometry for transformation of rotation between parallel axes are considered. Three types of topology of geometry are considered: (1) crowning of pinion tooth surface is provided only partially by application of a grinding disk; (2) double crowning of pinion tooth surface is obtained applying a grinding disk; (3) concave-convex pinion and gear tooth surfaces are provided (similar to Novikov-Wildhaber gears). Localization of bearing contact is provided for all three types of topology. Computerized TCA (Tooth Contact Analysis) is performed for all three types of topology to obtain: (i) path of contact on pinion and gear tooth surfaces; (ii) negative function of transmission errors for misaligned gear drives (that allows the contact ratio to be increased). Stress analysis is performed for the whole cycle of meshing. Finite element models of pinion and gear with several pairs of teeth are applied. A relative motion is imposed to the pinion model that allows friction between contact surfaces to be considered. Numerical examples have confirmed the advantages and disadvantages of the applied approaches for generation and design.

Mathematical Model for Parametric Tooth Surface of Cylindrical Gears Based on Kinematic Synthesis

2007 ◽  
Author(s):  
Carlos Garci´a-Masia´ ◽  
Juan D. Morillas-A´lvarez
Keyword(s):  
Mathematical Model ◽  
Tooth Surface ◽  
Asymmetry Ratio ◽  
Contact Ratio ◽  
Motion Generation ◽  
Kinematic Synthesis ◽  
Transmission Errors ◽  
Cylindrical Gears ◽  
Tooth Surfaces ◽  
And Function

A generalized approach for parametrizing conjugate tooth surfaces in cylindrical gears is presented in this work. Developed are the polynomials expressions to define the tooth surfaces of pinion and gear based on kinematics synthesis for planar gears. The polynomials expressions incorporate the motion generation (points or positions of precision) and function of transmission errors. It is interesting to note that if the desired pressure angle for the tooth profile is constant, the output polynomial of profile becomes a conventional involute. Polynomials expressions are given for the profile modifications necessary to compensate for any specified or anticipated errors of assembly and/or manufacturing. In addition property of rack as the limits of zone active, transverse contact ratio and contact asymmetry ratio are analysed.

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.

scholarly journals Computerized Design and Generation of Low-Noise Helical Gears with Modified Surface Topology

1995 ◽  
Vol 117 (2A) ◽  
pp. 254-261 ◽  
Author(s):  
F. L. Litvin ◽  
N. X. Chen ◽  
J. Lu ◽  
R. F. Handschuh
Keyword(s):  
Gear Tooth ◽  
Error Function ◽  
Transmission Error ◽  
Low Noise ◽  
Surface Topology ◽  
Helical Gears ◽  
Transmission Errors ◽  
Bearing Contact ◽  
Pinion Gear ◽  
Tooth Surfaces

An approach for the design and generation of low-noise helical gears with localized bearing contact is proposed. The approach is applied to double circular arc helical gears and modified involute helical gears. The reduction of noise and vibration is achieved by application of a predesigned parabolic function of transmission errors that is able to absorb a discontinuous linear function of transmission errors caused by misalignment. The localization of the bearing contact is achieved by the mismatch of pinion-gear tooth surfaces. Computerized simulation of meshing and contact of the designed gears demonstrated that the proposed approach will produce a pair of gears that has a parabolic transmission error function even when misalignment is present. Numerical examples for illustration of the developed approach are given.

Simulation Analysis of Contact Pattern and Strength of WN Gears Having Tooth Surface Deviations

2012 ◽  
Vol 479-481 ◽  
pp. 944-948 ◽  
Author(s):  
Dian Hua Chen ◽  
Zhong Wei Zhang
Keyword(s):  
Simulation Analysis ◽  
Practical Method ◽  
Transmission Error ◽  
Tooth Surface ◽  
Contact Pattern ◽  
The Finite Element Method ◽  
Tooth Contact Analysis ◽  
Surface Deviations ◽  
Tooth Surfaces ◽  
Loaded Tooth Contact Analysis

A practical method based on normal gaps topography is proposed here for loaded tooth contact analysis of WN gear having tooth surface deviations. The simulation of meshing state and tooth strength of WN gear are provided with real tooth surfaces. In the study normal gaps distribution is adopted to calculate tooth surface contact elastic deformation and local deviations due to manufacturing errors and tooth surface wear. For WN gear, the loaded distribution on the contact zone in meshing tooth surface has not been investigated because of their complexity in the contact state. The finite element method is adopted to analyze the contact pattern and tooth strength. The study has concretely calculated the contact pressure and zone of meshing in different loaded and transmission error. At the end examples are analyzed to demonstrate the effectiveness of the proposed method in quantifying effect of such deviations on the loaded distribution and tooth stress distribution.

scholarly journals An experimental method to measure gear tooth stiffness throughout and beyond the path of contact

2001 ◽  
Vol 215 (7) ◽  
pp. 793-803 ◽  
Author(s):  
R. G. Munro1 ◽  
D Palmer ◽  
L Morrish
Keyword(s):  
Gear Tooth ◽  
Contact Region ◽  
Transmission Error ◽  
Spur Gears ◽  
Contact Ratio ◽  
Extended Contact ◽  
Tooth Stiffness ◽  
Simplifying Assumptions ◽  
Tooth Pair ◽  
Usual Problem

A method is presented that allows the accurate measurement of the tooth pair stiffness of a pair of spur gears. The method reveals the stiffness behaviour throughout the full length of the normal path of contact and also into the extended contact region when tooth corner contact occurs. The method makes use of the properties of transmission error plots for mean and alternating components over a range of tooth loads (Harris maps). It avoids the usual problem when measuring tooth deflections that deflections of other test rig components are difficult to eliminate. Also included are predicted Harris maps for a pair of high contact ratio spur gears, showing the effects of various simplifying assumptions, together with a measured map.

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