and minimization of the dynamic loading of spur gears (original
Greek title: Ελαστοϋδροδυναμική λίπανση και ελαχιστοποίηση
δυναμικής καταπόνησης μετωπικών οδοντωτών τροχών ευθέων οδόντων)
Where: library of the Technical Chamber of Greece, 23-25 Lekka Street, 10562 Athens, Greece. The thesis (in Greek) was compiled in the School of Mechanical Engineering, National Technical University of Athens, Greece.
Author: George K. Nikas (National Technical University of Athens, School of Mechanical Engineering).
Supervisor: Dr Theodore Costopoulos (National Technical University of Athens, School of Mechanical Engineering).
Project duration: 12 months (1993-1994).
Thesis statistics: 187 pages, 44 figures, 118 detailed equations. The thesis is in the Greek language.
Download a PDF copy of this thesis in Greek (size: 41 MB)
Computer software developed:
Program EHL. Solution of the elastohydrodynamic problem for steady-state, line contacts and Newtonian fluids. Compiled in FORTRAN 77. Code length: 366 lines.
Program LOAD. Calculation of the static load distribution and corresponding tooth flank modifications in order to minimize the dynamic loading of spur gears with general tooth flank geometries. Compiled in FORTRAN 95. Code length: 1,055 lines. Latest version: 1.5.0.
This project was for the author's thesis for the Mechanical Engineering diploma and has two parts.
The first part of the project dealt with the modelling of the elastohydrodynamic lubrication (EHL) of spur gears with involute external teeth and the development of a solution algorithm for isothermal, steady-state conditions, Newtonian fluids and smooth contacts. The EHL algorithm is combined with a spur gear generalized geometrical analysis, which associates all geometrical parameters of spur gears with the matrix rack that "produced" them. It is, thus, possible to study the lubrication performance of spur gears by knowing the geometry of the rack, and alter this performance by modifying the geometry of the rack. In essence, this means that the required lubrication performance, loading and life of spur gears can be used as a design parameter and linked to the geometry of a single tool, namely the rack. This part of the project was published in:
Nikas, G. K., and Costopoulos, Th. Generalized Theory of Gearing and elastohydrodynamic lubrication of spur gears. In: Proceedings of the International Congress - Gear Transmissions 95, 26-28 September 1995, Sofia, Bulgaria, vol. 1, pp. 118-123.
The second part of the project dealt with the modelling of the dynamic loading of spur gears with involute external teeth and contact ratio less than 2. This type of gears suffers from abrupt changes of the transmitted load, owning to the continuous engagement and disengagement of teeth during a meshing cycle. The latter simply means that the contact load is transmitted alternatively by one pair and by two pairs of cooperating teeth, this succession being in force for as long as the cooperating gears rotate. Such a transient loading creates noise and vibrations of the whole gear system, including the supporting elements (bearings, axles, etc), which are unwanted and could cause premature failure of the gears themselves and/or other components. Having calculated the static load distribution (transmitted load during a meshing cycle), the next step is to optimise the teeth flanks in such a way that the aforementioned dynamic loading is minimized. This was achieved with accuracy for very high resolution of the teeth flanks (1000 points is sufficient) and, more importantly, the whole process requires an infinitesimal computing time (less than 1 second of CPU time). Even more importantly, the optimisation of the gear teeth was one of the design parameters of the gears, and can be done for any involute gears, inside or outside standard norms, and even for variable flank geometry due to manufacturing errors. The optimised gears can then be manufactured by precision CNC machining. This part of the project was published in:
Nikas, G. K. Load sharing and profile modification of spur gear teeth in the general case of any flank geometry. In: Proceedings of the International Conference on Gears, 22-24 April 1996, Dresden, Germany, VDI Berichte 1230, pp. 923-935.
Costopoulos, Th., and Nikas, G. K. Minimization of spur gear dynamic loading through the Generalized Theory of Gearing. In: Proceedings of the International Congress - Gear Transmissions 95, 26-28 September 1995, Sofia, Bulgaria, vol. 1, pp. 52-56.
Other publications based on this thesis
Nikas, G. K. Elastohydrodynamic lubrication - a qualitative approach to the problem. Journal of the Hellenic Association of Mechanical and Electrical Engineers, 1997, 302, 61-62. Featured article in Greek, based on the author's Diploma thesis; invited and edited by the Editor of the Journal.
Homepage of Dr Nikas