Vibro-Acoustic Analysis of Geared Systems—Predicting and Controlling the Whining Noise
The main source of excitation in gearboxes is generated by the meshing process. It is usually assumed that static transmission error (STE) and gear mesh stiffness fluctuations are responsible of noise radiated by the gearbox. They generate dynamic mesh forces which are transmitted to the housing through wheel bodies, shafts and bearings. Housing vibratory state is directly related to the noise radiated from the gearbox (whining noise). This work presents an efficient method to reduce the whining noise The two main strategies are to reduce the excitation source and to play on the solid-borne transfer of the generated vibration. STE results from both tooth deflection (depending of the teeth compliance) and tooth micro-geometries (voluntary profile modifications and manufacturing errors). Teeth compliance matrices are computed from a previous finite elements modeling of each toothed wheel. Then, the static equilibrium of the gear pair is computed for a set of successive positions of the driving wheel, in order to estimate static transmission error fluctuations. Finally, gear mesh stiffness fluctuations is deduced from STE obtained for different applied loads. The micro-geometry is a lever to diminish the excitation. Thus, a robust optimization of the tooth profile modifications is presented in order to reduce the STE fluctuations. The dynamic response is obtained by solving the parametric equations of motion in the frequency domain using a spectral iterative scheme, which reduces considerably the computation time. Indeed, the proposed method is efficient enough to allow a dispersion analysis or parametric studies. The inputs are the excitation sources previously computed and the modal basis of the whole gearbox, obtained by a finite element method and including gears, shafts, bearings and housing. All the different parts of this global approach have been validated with comparison to experimental data, and lead to a satisfactory correlation.
KeywordsVibro-acoustic Gear mesh dynamics Gear optimization Whining noise
This work was supported by the French National Research Agency through the research project MABCA (ANR 08-VTT_07-02). The partners involved were VIBRATEC, LTDS-Ecole Centrale de Lyon, RENAULT and RENAULT TRUCKS. The authors want to thank especially J. Vialonga from Renault technical center of Lardy (France) and D. Barday from Renault Trucks for their scientific and technical supports and for the shared data.
The French National Research Agency has also supported through the joint laboratory LADAGE (ANR-14-Lab6-003) issued from the collaboration between LTDS-Ecole Centrale de Lyon and VIBRATEC.
- 2.Remond D, Velex P, Sabot J et al (1993) Comportement dynamique et acoustique des transmissions par engrenages. Synthèse bibliographiqueGoogle Scholar
- 3.Welbourn DB (1979) Fundamental knowledge of gear noise—a survey. Proc Conf Noise Vib Eng Trans C177/79:9–29Google Scholar
- 5.Beghini M et al (2004) A method to define profile modification of spur gear and minimize the transmission error. In: Proceedings AGMA fall meetingGoogle Scholar
- 7.Carbonelli A et al (2011) Particle swarm optimization as an efficient computational method in order to minimize vibrations of multi-mesh gears transmission. In: 2011 advances in acoustics and vibrationGoogle Scholar
- 8.Eberhart RC, Kennedy J (1995) A new optimizer using particle swarm theory. In: Proceedings of the sixth international symposium on micro machine and human science. IEEE Service Center. Piscataway, pp 39–43Google Scholar
- 9.Nonaka T, Kubo A, Kato S, Ohmori T (1992) Silent gear design for mass produced gears with scratters in tooth accuracy. In: ASME proceedings of the international power transmission and gearing conference, Scottdale, USA, vol 2, pp 589–595Google Scholar
- 10.Driot N, Rigaud E, Sabot J, Perret-Liaudet J (2001) Allocation of gear tolerances to minimize gearbox noise variability. Acustica United Acta Acustica 87:67–76Google Scholar
- 11.Perret-Liaudet J (1992) Etude des Mécanismes de Transfert entre l’Erreur de Transmission et la Réponse Dynamique des Boîtes de Vitesses Automobiles. Thèse de doctorat de l’Ecole Centrale de Lyon N°9207ʺGoogle Scholar
- 13.Carbonelli A (2008) Caractérisation vibro-acoustique d’un cascade de distribution poids lourd. Thèse de doctorat de l’Ecole Centrale de Lyon N°2012-34ʺGoogle Scholar
- 14.Rigaud E, Barday D (1998) Modeling and analysis of static transmission error of gears: effect of wheel body deformation and interactions between adjacent loaded teeth. Mécanique Industrielle et Matériaux. 51(2):58–60Google Scholar
- 15.Rigaud E, Barday D (1999) Modelling and analysis of static transmission error. Effect of wheel body deformation and interactions between adjacent loaded teeth. In: 4th world congress on gearing and power transmission, Paris, vol 3, pp 1961–1972Google Scholar
- 17.Clerc M (1999) The swarm and the queen: towards a deterministic and adaptive particle swarm optimization. In: Proceedings of ICEC, Washington, pp 1951–1957Google Scholar
- 18.Åkerblom M, Sellgren U (2008), Gearbox noise and vibration—influence of bearing preload, MWL, Department of Vehicle Engineering, KTH, SE–100 44 Stockholm urn University, Auburn, Alabama 36849, USA Google Scholar