外文翻译Reduction of noise of loaded and unloaded misaligned gear drivesFaydor L. Litvina, Daniele Vecchiatoa, Kenji Yukishimaa, Alfonso Fuentesb, Ignacio Gonzalez-Perezb and Kenichi Hayasakac aGear Research Center, Department of Mechanical and Industrial Engineering, University of Illinois at Chicago, 842 W. Taylor St., Chicago, IL 60607-7022, USAbDepartment of Mechanical Engineering, Polytechnic University of Cartagena, C/Doctor Fleming, s/n, 30202, Cartagena, Murcia, SpaincGear R&D Group, Research and Development Center, Yamaha Motor Co., Ltd., 2500 Shingai, Iwata, Shizuoka 438-8501, Japan Received 22 February 2005; revised 6 May 2005; accepted 17 May 2005. Available online 25 January 2006.AbstractTransmission errors are considered as the main source of vibration and noise of gear drives. The impact of two main functions of transmission errors on noise is investigated: (i) a linear one, caused by errors of alignment, and (ii) a predesigned parabolic function of transmission errors, applied for reduction of noise. It is shown that a linear function of transmission errors is accompanied with edge contact, and then inside the cycle of meshing, the meshing becomes a mixed one: (i) as surface-to-surface tangency, and (ii) surface-to-curve meshing when edge contact starts. Application of a predesigned parabolic function of transmission errors enables to absorb the linear functions of transmission errors caused by errors of alignment, reduce noise, and avoid edge contact. The influence of the load on the function of transmission errors is investigated. Elastic deformations of teeth enable to reduce the maximal transmission errors in loaded gear drives. Computerized simulation of meshing and contact is developed for loaded and unloaded gear drives. Numerical examples for illustration of the developed theory are provided. Keywords: Gear drives; Transmission errors; Tooth contact analysis (TCA); Finite element analysis; Reduction of noise 1. IntroductionSimulation of meshing of gear drives performed by application of tooth contact analysis (TCA) and test of gear drives have confirmed that transmission errors are the main source of vibrations of the gear box and such vibrations cause the noise of gear drive 1, 2, 4, 5, 6, 7, 10 and 11. The shape of functions of transmission errors depends on the type of errors of alignment and on the way of modification of gear tooth surfaces performed for improvement of the drive (see Section 2). The reduction of noise proposed by the authors is achieved as follows: (1) The bearing contact of tooth surfaces is localized.(2) A parabolic function of transmission errors is provided. This allows to absorb linear functions of transmission errors caused by misalignment 7.(3) One of the pair of mating surfaces is modified by double-crowning (see Section 2). This allows usually to avoid edge contact (see Section 5).The authors have compared the results of application of TCA for loaded and unloaded gear drives. It is shown that transmission errors of a loaded gear drive are reduced. The developed approach is illustrated with numerical examples (see Section 5). 2. Modification of tooth surfacesReduction of noise of a gear drive requires modification of one of the pair of contacting surfaces. The surface modification is illustrated for three types of gear drives: helical gears, spiral bevel gears, and worm gear drives. 2.1. Helical gear drivesProfile crowning of helical gears may be illustrated considering that the mating surfaces are generated by two rack-cutters with mismatched profiles 5 and 7. Profile crowning allows to localize the bearing contact. Double-crowning in comparison with profile crowning allows to: (i) avoid edge contact (caused by errors of crossing angle and different helix angles of mating gears), and (ii) provide a parabolic function of transmission errors. Double-crowning is performed by plunging of the disk that generates the pinion (see details in Chapter 15 of Ref. 7).2.2. Spiral bevel gearsLocalization of contact of generated spiral bevel gears is provided by application of two mismatched head-cutters p and g used for generation of the pinion and the gear, respectively 7. Two head-cutters p and g have a common line C of generating tooth surfaces (in the case when profile crowning is provided). In the case of double-crowning, the mismatched generating surfaces p and g of the head-cutters have only a common single point of tangency, but not a line of tangency. Double-crowning of a generated gear may be achieved by tilting of one of the pair of generating head-cutters, or by proper installment of one of the head-cutters. It is very popular for the modern technology that during the generation of one of the mating gears, usually of the pinion, modified roll is provided 7. 2.3. Worm gear drives with cylindrical wormVery often the technology of manufacturing of a worm-gear is based on the