AGMA 90FTM6-1990 pdf free.Dynamic Responses of Aircraft Gears.
The study of natural frequencies is a well-developed branch of engineering. F4any publications have been released on the subject of the application for practical engineering analysis, such as; Theory of Elasticity by Timeshenko and Goodler (1), Nathernatical Theory of Elasticity by Sokolnikoff (2), Nechanical Vibrations by Den Hortog (3), A Treatise on the Mathematical Theory of Elasticity by Love (4), or publications of Peterson (5), Alford (6), Drago (1), TuplIn (8), and A6MA (9).
The governing equations of natural frequency, as used in gear resonance analysis, dates back to definition of concepts of elasticity and Stress wave propagation by Pythagorean and Aristotlean. Equations and theories later on refined by Galileo 1638, Robert Hooke 1618, Isac Newton 1686, Thomas Young 1801, Cauchy 1822, Novier 1821, Green 1827, Lord Rayleigh 1817.
As the 20th Century approached, theories of vibrations began to advance rapidly and separated from the dynamics of elastic materials. Basically, the equations we now use and call the edge of technology were mathematically derived and verified by large scale tests at the beginning of this century.
BACKGROUND
Resonance phenomena in gears is complex in understanding. However, elementary equations which guide the design of high power density aerospace gearing can be derived directly from the equations of motion and by using certain simplifying assumptions.
One of the earliest successful efforts to apply the elementary equations to resonance phenomena of three dimensional solids were developed by Love. The treatment takes Into account the inertia of lateral contraction. The loves assumtlon are retained that plane sections remain plane and longitudinal vibrations or stresses over a cross section is uniform.
The aircraft gears, in concern, generally consists of two geometrical shapes, the disk a’d the ring. Exiting frequency of solid pinions are usually beyond the range of their operation. Nowever, bevel and beveloid gears which are basically disks and the bull or internal gears which are basically ring or finite cylinder coupled with thin disks are often being exited, at frequencies close to one of their resonant frequencies and during the operation
We must be alert, during examination of high frequency waves, ft Is 1iortant to distinguish between the higher order harmonics of the simple modes and lower order harmonics of higher modes. Both consists of high frequency vibrations, but the resultant motions are physically very different.
With respect to the understanding of the higher modes of vibration, we can examine the nodal planes passing through the axis of the :ylinder. A circular cylinder vibrating in the nth mode may be considered as consisting of n pairs ol diametrically opposite sectors of a circle. The n pairs of sectors may be chosen In two ways, either bounded by nodal planes of radial motion or nodal planes of angular notion. These planes are separated by an angle (w/2n). AGMA 90FTM6 pdf download.