On the analytical definition of profile modifications minimising transmission error variations in narrow-faced spur helical gears

Abstract Two original analytical formulations are presented which explicitly give the depths and extents of symmetric profile modifications minimising the fluctuations of quasi-static transmission error in narrow-faced spur and helical gears. Numerous comparisons with quasi-static and dynamic simulation results are presented which prove that the proposed theory is sound. The proposed formulae can therefore help define adapted reliefs in terms of transmission error and dynamic tooth loading with minimum effort.

[1]  Donald R. Houser,et al.  Optimum Profile Modifications for the Minimization of Static Transmission Errors of Spur Gears , 1986 .

[2]  R. G. Munro,et al.  Dynamic Behaviour of Spur Gears , 1963 .

[3]  Philippe Velex,et al.  Derivation of Optimum Profile Modifications in Narrow-Faced Spur and Helical Gears Using a Perturbation Method , 2013 .

[4]  Philippe Velex,et al.  A simplified multi-objective analysis of optimum profile modifications in spur and helical gears , 2014 .

[5]  R G Munro,et al.  A systematic approach to profile relief design of low and high contact ratio spur gears , 1999 .

[6]  久保 愛三,et al.  超高速歯車装置に関する研究 : 第1報,超高速歯車試験機の運転特性 , 1972 .

[7]  Donald R. Houser,et al.  A MULTI-VARIABLE APPROACH TO DETERMINING THE "BEST" GEAR DESIGN , 2000 .

[8]  Donald R. Houser,et al.  Some Analytical Results on Transmission Errors in Narrow-Faced Spur and Helical Gears: Influence of Profile Modifications , 2011 .

[9]  Hsiang Hsi Lin,et al.  Dynamic Loading of Spur Gears with Linear or Parabolic Tooth Profile Modifications , 1994 .

[10]  R. Cornell.  Compliance and Stress Sensitivity of Spur Gear Teeth , 1981 .

[11]  P. Velex,et al.  Quasi-Static and Dynamic Analysis of Narrow-Faced Helical Gears With Profile and Lead Modifications , 1997 .

[12]  Aizoh Kubo,et al.  Analysis of General Characteristics of Transmission Error of Gears With Convex Modification of Tooth Flank Form Considering Elastic Deformation Under Load , 2009 .

[13]  G. Lundberg.  Elastische Berührung zweier Halbräume , 1939 .

[14]  Donald R. Houser,et al.  A Procedure Using Manufacturing Variance to Design Gears With Minimum Transmission Error , 1991 .

[15]  José I. Pedrero,et al.  Load distribution model along the line of contact for involute external gears , 2010 .

[16]  Rajendra Singh,et al.  Non-linear dynamics of a spur gear pair , 1990 .

[17]  K. Ishii,et al.  Design optimization for robustness using performance simulation programs , 1992 .

[18]  Y. Terauchi,et al.  ON THE EFFECT OF THE TOOTH PROFILE MODIFICATION ON THE DYNAMIC LOAD AND THE SOUND LEVEL OF THE SPUR GEAR , 1982 .

[19]  Hsiang Hsi Lin,et al.  Influence of Linear Profile Modification and Loading Conditions on The Dynamic Tooth Load and Stress of High-Contact-Ratio Spur Gears , 1991 .

[20]  Kiyohiko Umezawa,et al.  Effects of Contact Ratio and Profile Correction on Gear Rotational Vibration , 1983 .

[21]  Ian Howard,et al.  The torsional stiffness of involute spur gears , 2004 .

[22]  P. Velex,et al.  Static and Dynamic Tooth Loading in Spur and Helical Geared Systems-Experiments and Model Validation , 2002 .

[23]  Ahmet Kahraman,et al.  Effect of Involute Tip Relief on Dynamic Response of Spur Gear Pairs , 1999 .

[24]  Niels Leergaard Pedersen,et al.  On gear tooth stiffness evaluation , 2014 .

[25]  P. Velex,et al.  A MATHEMATICAL MODEL FOR ANALYZING THE INFLUENCE OF SHAPE DEVIATIONS AND MOUNTING ERRORS ON GEAR DYNAMIC BEHAVIOUR , 1996 .

[26]  Donald R. Houser,et al.  Mathematical models used in gear dynamics—A review , 1988 .