Abstract
The dynamic response of gearbox remains a paramount concern because of noise generation. This work is concerned with numerical simulation of the overall dynamic behaviour of a parallel helical gear transmission. A dynamic sub-structuring method using different types of substructure (carrying and slave) is made to determine the natural frequencies and the corresponding mode shapes. The structure to be investigated is subdivided into components or sub-structures, which are then analyzed independently for natural frequencies and mode shapes. A numerical model taking into account the elastic coupling between the various components of a gearbox was developed. It allows studying and analyzing the dynamic behaviour of elastic housing in the presence of gear process. The static transmission error is introduced as a vibratory excitation source and it is represented by time-varying mesh stiffness. The discretization of the housing deformation energy and the kinetic energy expressions using plate finite elements leads to constructions of the stiffness and the mass matrixes. In dynamic analyses, time-discretization based on the Newmark method is used. The different equations governing movement of gearbox are established in a truncated modal base deduced from the average characteristics of the structure. A gearbox example is presented, and analyzed. A presentation and discussion of the numerical results was emphasized. The numerical results allow us to conclude on the dominant phenomena of the overall dynamic behaviour of the gear transmission.
Similar content being viewed by others
References
Zakrajsek J, Oswald BF, Townsend PD, Coy JJ (1990) Gear noise, vibration, and diagnostic. Studied at NASA Lewis Research Centre. NASA, TM-102435
Ozguven HN, Houser DR (1988) Mathematical-models used in gear dynamics. J Sound Vib 121:383–660
Rigaud E, Sabot J, Perret-Liaudet J (2000) Approche globale pour l’analyse de la réponse vibratoire d’une transmission par engrenages. Revue Européenne des Eléments Finis 9:315–330
Rigaud E, Barday D (1999) Modelling and analysis of wheel body deformation and interactions between adjacent loaded teeth. 4th World Congress on Gearing and Power Transmission, Paris 3:1961–1972
Seybert AF, Oswald FB (1992) Acouctical analysis of gear housing vibration. Nasa TM-103691
Lim TC, Singh R (1989) A review of gear housing dynamics and acoustics literature. Nasa CR-185148 Technical Memorandum 89-C-009
Sabot J, Perret-Liaudet J (1992) Computation of the noise radiated gearbox. International Gearing Conference
Haddar M (1998) Réponse Dynamique d’une Boite de Vitesse. Rev Int Ing Syst Prod Mec 1:29–34
Hou SN (1969) Review of modal synthesis technique and a new approach. Shock Vib Bull 40:25–39
Craig RR, Bampton MCC (1968) Coupling of substructures for dynamic analysis. A.I.A.A J 6(7):1313–1319
Hurty WC (1965) Dynamic analysis of structural systems using component modes. AIAA J 3:678–685
Todd E (1996) Mobility analysis of structure-borne noise power flow through bearings in gearbox-like structures. Noise Control Eng J 44(2)69–78
Bourdon A (1995) Modelisation Dynamique Globle des Boites de Vitesse Automobile. Dissertation, INSA. Lyon
Velex P (1988) Contribution à l’Analyse du Comportement Dynamique de Réducteurs à Engrenages à axes Parallèles. Dissertation, Institut National des Sciences Appliquées de Lyon, No 88, ISAL 0032
Lin J, Parker RG (2002) Mesh stiffness variation instabilities in two-stage gear systems. Trans ASME 124(1):68–76
Batoz JL, Dhatt G(1990) Modélisation des Structures par Eléments Finis Poutres et Plaques. Edition Hermes, Paris
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Abbes, M.S., Fakhfakh, T., Haddar, M. et al. Effect of transmission error on the dynamic behaviour of gearbox housing. Int J Adv Manuf Technol 34, 211–218 (2007). https://doi.org/10.1007/s00170-006-0582-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00170-006-0582-7